There's already a thread from SAO but it's pretty dead so I thought I'd make this compound thread. First, some synopses!
Sword Art Online: The players of a virtual reality MMORPG, Aincrad Online, are trapped and fighting for their very lives. After it is announced that the only way to leave the game is by beating it, Kirito—a very powerful swordsman—and his friends take on a quest to free all the minds trapped in Aincrad.
Accel World: In 2046, people can access a virtual network known as the Neurolinker via their cellphone terminals. A perpetual victim of bullying, middle school student Haruyuki spends his time absorbed in games in a corner of his local network. One day he is approached by the most famous girl in his school, Kuroyukihime (Black Snow Princess). She gives him a strange program called Brain Burst that has the power to "accelerate the world."
Both of these are written by the same author, and if you follow the SAO light novels then you'll start to see some small cross over explanations. The animation quality for both anime is pretty high quality imo. There's plenty of action everywhere and you can watch these shows purely to enjoy the fights if you want. I'd definitely recommend watching both of these shows.
However the light novels are also good. The accel world anime covers volumes 1-4 of the light novel material, and there are 12 volumes out right now. Only volumes 1-4 are translated and can be found at baka-tsuki. Sword Art Online currently has 11 volumes and they are all fully translated. The anime covers volumes 1-4 there as well. Volume 12 of SAO is scheduled to come out in April. After watching SAO I'd highly, highly recommend reading SAO.
I'll probably throw some more info into this thread later to hype it up some more. Somebody throw in some images and gifs. :3
Edited, Feb 18th 2013 11:31am by Deadgye