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Generally speaking, with the way the game is set up currently, gaining reputation in the most efficient way isn't necessarily anything to really worry about. Getting to Honored with most factions (which will allow the purchase of some tradeskill recipes, allow the purchase of Heroic keys and ability to buy some armor and weapons) is farily easy to do just through general questing.
However, there can be times where you want to progress to Revered or Exalted in order to purchase better items like epic patterns or recipes, head glyphs or epic weapons and armor. Getting to revered or exalted, while not hugely difficult, can be made easier with a little planning.
Generally this article is dealing with Outland/Burning Crusade repuation, but the premise still holds true on some of the original Azerothian factions.
For specific information on what may be useful to your class/spec or your professions, see the section about Targeted Rep Items and follow the links to your area of interest.
The first rule, really the only rule, in trying to reach the higher levels of reputation is take full advantage of repeatable quests and take advantage of them first. What this means is, when you're trying to gain reputation with a faction don't just rush out and do all the regular quests first thinking you'll make it up any shortfall with the repeatable ones later. Often the repeatable quests can only be turned in up to a certain reputation level so by the time you finish all of the other quests, the repeatable ones are no longer available to you.
In Outland this typically happens at Honored (technically 1 point below Honored as the repeatable quests will not bump you up to Honored). Often these quests are gathering-style quests like the Lower City rep quest More Arakkoa Feathers or the Cenarion Expedition's Identify Plant Parts.
Basically what you want to do if you're frming Lower City or Cenarion Expedition rep (for example) is collect all of the plant parts or feathers than you can to get yourself 1 point from turning Honored and only then start on quests that will give Cenarion Expedition rep specifically.
If you're trying to get to Exalted in order to get a different faction's mount then things are a little different though it's still most beneficial if you plan ahead.
The first thing that you want to do is make certain that you can actually use the mount that you're trying for. For example, only Gnomes and Dwarves can use the mechanical chicken mount so if you're a human it's not even worth trying.
Gaining reputation for the purposes of a mount works better the earlier you start because the reputation gains from quests can drop as you get higher in level. So if you've made the decision to switch and get another race's mount at 35 it's going to be more difficult than if you had made the decision at level 10.
Basically when you're going after a racial mount it's easiest if you go back to their beginning areas (or move to them from your own between levels 6-10, you can't do the very beginning quests) and do every quest that's offered in that area. If you keep progressing through the specific race's questing areas that will get you a long ways toward your mount. But note also that, once you've gained some rep with them, any of quests that give racial reputation to a specific race will also give a fraction of the reputation to all of the other races. So while a focus on the target race is importat it can also be beneficial to do other quests as well.
Generally speaking all other reputations (with the exception of the Bloodsail Buccaneers for the Bloodsail Admiral's Hat is not an either/or thing. You can work your way to exalted with the Consortium, Cenarion Expedition, Sha'tar, etc all at the same time. The exception to this is the Aldor and Scryer factions. You must choose one or the other and you cannot receive the benefits of both.
This always leads to the question of the new level 60 who's take the Shattrath Tour "So which do I choose?". That question, just by itself like that, is not something anyone can answer. It depends on a variety of factors.
The general impression from players is that Scryers tend to give rewards, armor and glyphs that favor damage dealing while Aldor seem to have more defensive rewards.
Your class and spec, however, shouldn't necessarily be the only consideration. Each side offers different tradeskill recpies which may be more useful or important than any quest rewards or armor purchases depending on your focus.
Additionally, it should be noted that the reputation gaining items for the Scryers (namely the Sunfury Signet and the Arcane Tome seem to be much easer to come by than the Aldor Mark of Sargeras and Fel Armament. Whether that's because they truly do drop more or because they are in higher traffic areas due to other quests and popular instances is up for debate, but it is true that more Scryer items are looted (according to the World of Warcraft Top Looted List) than Aldor.
There are several things to consider when making your choice. Note that it is possible to reverse your choice later by performing repeatble quests, but those are a significant grind so a reasoned initial choice is worth making. For more information and item comparisons see: Aldor Scryer Comparison.