Yes, quest content gets boring after a while. We all know that there are only three types of quests - kill, collect, and deliver. When you get down to it though, there isn't much else that can be done that will actually work. Suggest all you want, there's probably a reason your idea hasn't been tried, and not because nobody thought of it. At least every quest has a unique storyline. (Or someone asks you to collect something stupid for a stupid reason, usually a cook. Cooks seem to put anything imaginable and then some into their food...I really couldn't stomach Azeroth cuisine.)
Nevertheless, the quests in the game are what make the game interesting and keep the player feeling like they have a purpose beyond just whack this killer rabbit here, that single-celled organism there.
Many people at lower levels (pre-20) complain that the game is World of Solocraft. Ironically people at the higher-end often have issue with finding things they can do on their own besides just kill random mobs. The questing content in this game progressively switches from almost exclusively solo to largely group-based as you level.
Quests are sometimes marked "group", which means that the creatures involved in the quest are elites -- much more difficult mobs than their level would indicate. (They don't just raise the level because that level would make them harder to hit.) Group quests are basically specially marked as group content. Does this mean you shouldn't group for non-group quests?
If you do have a decent group, and finish one quest, you might consider asking if any of them have some of the same quests you still need to finish in the area. Very often, at least one other person will agree to work on it. You can usually tell how many people in your party have a quest by looking at your quest log - a number in bracket will show up beside any quest that other party member are also on.
The one annoying thing about grouping for quests is trying to move on to another quest and finding not everyone has the quest. Fortunately, there is a solution. Unfortunately, it doesn't always work. That solution is quest sharing -- if a person could have a quest but simply doesn't, you can go into your quest log and press "share quest" to transmit it to them, as though they were talking to the quest NPC for the first time. But if the other person is too low to get the quest, or your quest is one of the later legs in a chain, they won't be able to get it.
Still, this can be used to your advantage. People going to an instance together can share the quests for it before starting, which are often from all different corners of the earth. If you are agreeing to meet a friend in a new zone, and one of you gets there first, they can hunt for the questgivers until the other person arrives.
If you are forming a group in advance to try to do a particular quest (or other objective) because it is too difficult to do alone, you will probably want to consider class roles. 5 priests can do a lot, but one thing they can't do is tank the mobs that come at them or do a whole lot to otherwise stop them. On the other hand, 5 warriors could survive a more fierce beating, but they'll have to stop to eat after each fight, and hope nobody dies during the battle.
You can have five people in a group, and usually you will want at least one "tank" and one healer. Tanks are usually warriors, but can be anyone who is capable of standing up front and taking the blows from your foes. Main healers for groups need to be reasonably capable of keeping the group alive through all normal situations by themselves. Keep in mind that "normal" includes the rest of the group being accommodating and playing with good tactics. Mages take more mana to heal than the group's tank, and if a mage is constantly drawing the attention of the creature, the healer will run out of gas much more quickly.
Other players generally fill the role of dealing damage. They may have secondary responsibilities, like being the back-up healer or tank, or performing crowd control. For this reason, mages are very popular in groups, because they can deal a lot of damage, and also CC by casting polymorph to remove one creature from the fight (assuming nobody hits it!)
Some players are very elitist in which classes they will take in their group, and others are overly forgiving in this regard. You usually want your group to be well-balanced, but you shouldn't wait all day long and turn people away to get the "perfect" group. Every class brings something to the table.
Instanced dungeons, or instances, are special areas that you enter through a portal, and arrive in your own special copy of that area. Only your group members will follow you into it; anyone else that tries will be in a second copy.
Instances are full of elite mobs that are worth more exp, generally yield better treasure, and lead to good teamwork to overcome higher difficulty. Most players find doing instances to be more fun than playing by themselves, however they can also be EXTREMELY frustrating in an incompetent group.
There are almost no instances before level 20. Considering they make up the bulk of group content in the game, know what you have to look forward to. The Horde does have one low-level instance inside Orgrimmar called Rage Fire Chasm. The first instance the Alliance can do is the Deadmines in Westfall, at no less than 18.
Assist. Assist. Assist. By default, pressing F will give you the target of the person (or creature) you have targeted. It's usually a better idea for everyone to attack the same creature to kill it faster, since you will normally not have one by itself. Being a hero and fighting something by yourself does NOT help the group in most cases.
"Pulling" is the act of getting a creature's attention and bringing it to the group. Rather than charging ahead, let one person "pull" in an organized manner, and follow their lead. Most of the time this will be the warrior. (I'm going to assume you have a warrior tank.) Doing otherwise will often lead to unnecessary overpulls - fights involving more creatures than you really needed to take on at once and usually can't handle.
Use crowd control as you are able. If a rogue can sap a target to start a fight, let them. Don't hit the person the mage turns into a sheep and break the enchantment.
Control your aggro. Aggro is the MMO player's term for the amount of hate your target has built up toward you. (The in-game terms refer to this as threat.) When you have more aggro than anyone else, you become the creature's target. If you are not the group tank, this means something is not going the way it should. If you are a mage, don't nuke your pants off from the moment the fight begins. Be aware of which skills generate a high amount of aggro (like Mind Blast and Distracting Shot.)
Know your role. Every player needs to consider the things they CAN do reasonably, and the things the group EXPECTS them to do. The group's tank needs to concentrate his efforts on holding aggro. In other games, this has meant the tank has done nothing but devote themselves to this task. Blizzard has tried to make the game slightly less boring for the tank, but if you are a warrior, expect to have to use taunt. Similarly, the group's healer needs to keep in mind that if they have the choice to cast one damage spell or one healing spell, that mana is usually better spent on a healing spell that keeps the group alive longer, because the extra time it buys usually lets the group outdamage your one nuke. Again, this doesn't mean a healer should stand around placidly waiting for someone to heal, but don't be reckless.
Keep your healer alive. There is one key exception to many of the rules above. Take whatever means necessary to keep people from dying. Since the group healer is largely responsible for keeping everyone else alive, it is the responsibility of the rest of the group to keep him or her safe. Keep in mind that the act of healing creates hate. If a priest casts a healing spell on whoever just pulled three mobs, even if they are actively fighting one, if they have built up no hate toward the other two by damaging it or using other abilities, they will make a beeline for the priest. A player being hit usually cannot cast spells effectively, so this means nobody else is getting healed, and since priests in particular wear cloth armor, they probably won't survive being wailed on for very long. (I've been killed in one blow before.) On the other hand, if you are the healer, consider the strategic timing of your heals, and don't yell to the group the split second something attacks you -- they might be in the process of reacting already and a priest that says "Help me!" every three seconds gets annoying very quickly.
Discuss loot in advance. This can vary greatly depending on who you're with - a group of friends might have one set policy, but when dealing with strangers you don't know or trust, you might adopt a different policy. The group leader has the ability to change the way the game distributes items that drop, but that doesn't make them the dictator of how loot works, nor does it explain all situations. See bosses and boss loot below. Round robin or group loot with an implied understanding of need before greed is the usual player standard.
Help first-timers. Make sure they know where a dungeon actually is, but also there are often nuances to dungeons that someone that has never been there would not know. Gnomeregan has an alarm system that sometimes needs to be deactivated before it summons a bunch of defense forces to drive you away. Some interactive objects cause events to occur that the group might not be ready for, and a curious player might unwittingly undermine the group's efforts. Don't talk down to your group, but make sure they're on the same page.
Consider the group's goals. Sometimes this is to finish a particular quest in the dungeon. Often it is to kill the major "named" bosses and collect their treasure. Make sure everyone agrees to the group for the same reasons.
Deal with bosses carefully, and deal with their loot afterwards even more carefully. Pre-battle strategy discussion is even more important on named. Moreso, the downfall of a great group is often a squabble over loot that keeps them from finishing the dungeon after one mini-boss. Items that drop from bosses are BIND ON EQUIP. You pick it up, you will be unable to trade it. If someone feels you stole an item, that won't be good for your reputation. More to the point is the subject of giving items to people who need them. In a group with a rogue, a mage, and a paladin, suppose a nice dagger with a bonus to agility drops. The paladin is clearly out because he can't even equip daggers. But the mage, although he *could* use the item, should let the rogue take it if it is an upgrade, because the agility does the mage little good and neither does the weapon damage, which to a rogue is everything. (If that rogue has a better item, they should abstain as well.) If you are a warrior in the upper 20's, and you don't have a head slot item, you should NOT claim a cloth item with an intelligence bonus for the *piddly* armor it has on it. If a leather item with agility drops, a paladin should not be the least bit interested in it unless there is something else special about it. The in-game need before greed loot system is not the standard, because it doesn't consider such things. If nobody can use an item, the generally accepted practice is to roll for it by typing /random, with the highest roller winning. *MOST* groups work with an implicit understanding that once you win something, you do not take another item until everyone gets something. Whether or not they regard a loot item and a cash item as part of the same cycle or not depends on the group.
Help supply your groupmates. Within reason, of course. Nobody expects you to farm herbs for hours just to give away all your healing potions. But at the very least, a mage should give out free summoned food and drink.
Don't get mad when you die. There's only one truth about war: people die. While you may not like it when it happens, and you might have some choice words for a groupmate who did something stupid that caused that death, don't throw a hissy fit. Shut up, run back or wait for your rez, and talk about it like a civil human being. "OMG WTF U GAY FGT N00b" is not going to help the issue, both because of the tone and message, and because half the people in your group won't be able to understand you in the first place. Also don't bail out just because you don't like the way things are going. (If a group is completely worthless, make an exception, but give them a fair chance. If you don't help them, they'll never improve.)
Don't be upset if someone has to leave. Some instances, like the Stockades, can be done in 45 minutes. Others can take much longer, especially if the pace of the group is slow. Not everyone can devote more than 3 hours at a stretch to playing an internet game. (It's a strange concept to anyone still in school, but it's true!)
Don't join a group if you don't have time. If you only have an hour, chances are you won't be able to finish the instance. If you can *never* play for more than an hour at a time...I'm sorry. Instances are not for you. They are meant to be fast-paced high-challenge adventures for people with the time to devote to such an adventure.
So what about those times you want to have more than 5 people, and do something challenging, like take on a dragon?
That's what raids are for. Under your socials menu, there is a tab labeled raid, and in it, the group leader can select the option "convert to raid" to allow him to invite additional people beyond the 5-person limit. They start filling additional groups until all 8 in the window are full. The raid leader can rearrange people from group to group as he sees fit.
Raids have their own channel, /raid, that works in addition to /party to just talk to your most immediate teammates. Besides that, raids work just like groups, with a couple key exceptions:
Raids cannot enter some instances as a whole. This would trivialize the content, as was found to be the case when raids were first put into beta, and 30 level 15 players formed a mob to simply zerg the Deadmines.
Raids cannot complete quests. If you form a raid in an outdoor zone to finish a kill quest for a large group, you will be disappointed. No kills are accredited, and no quest items will drop.
Raids, by their nature, can do things a mere 5-person group could not. This goes without saying -- maybe a lone adventurer can't kill a dragon, but an army probably could. To that effect, there are special instances that are designed just for raiding. This is almost exclusively max-level content, and is something high-end players look forward to.