For what it's worth, added my additional opinions in italics, given what I've seen:
Baka to Test to Shoukanju - Idiots and tests and summoning things. People are put into class according to their grades. Their latest test scores become the power of their familiar. It's like Yu-gi-oh GX but focuses more on humor than battles. I loved this show and it was only 13 episodes. Watch it.
~ Alternated repeatedly between amazingly clever and awesome episodes and completely stupid "why am i watching this" episodes. On the whole, not bad, especially since there's only 13 episodes.Black★Rock Shooter - OVA It's hard to really explain. It's just 50 minutes long as I recall. Give it a go some night.
~ I didn't know anything about it besides the actual song when I watched it, and yeah, it's hard to explain and/or understand and/or whatever, but at 50 minutes for the entire thing it's worth an hour I think.Canaan - Another great show. This one is extremely hard to explain as well. It's good and it keeps a mostly realistic setting as well. I guess all I can really say about this show is... SUGOI
~ Really hard to explain, yeah. I mean, I guess not, but it would spoil a lot of plot. SUGOI is a pretty good explanation.Disappearance of Haruhi Suzumiya - Haruhi movie. Watch after Season 2 of Melancholy of Haruhi Suzumiya
~ Yep!Highschool of the Dead - Zombies take over the world. Some highschoolers have to survive and find shelter. You might be better off reading the manga. I don't think this one is getting a second season.
~ SO TERRIBLE. I haven't seen the manga but it HAS to be better.K-ON! - Highschool girls in a music club. It's really good I swear. There's just no cool way to describe it. It's honestly one of my favorite series and I look forward to the movie.
~ Much better than I expected it to be, given that Pyro wouldn't even try describing it when I asked. Let me try. "Highschool girls in a music club." Yeah, that works.K-ON!! - See above. I cried a little when it ended. I wish there was more.
~ Me too. 
Nyan Koi - Guy is cursed by cats and has to help them or he'll turn into a cat himself. He's also allergic to them.
~ Like 100 Deeds for Eddie McDowd or whatever it was except with cats and animated and the guy's not a total jerk! I think. I never actually watched that show on Nickelodeon.Sayounara Zetsubou Sensai - Teacher that is always in despair and wants to die. He teaches a group of children that cover just about every stereotype in the book. Was a hilarious show and I wish they'd make a 4th season.
~ Don't really recall; it was the second anime I ever watched. It was okay at the time but for some reason I never watched more than the first season.To Aru Majutsu no Index - Guy with misfortune gets more misfortune as he's stuck with a small girl that contains 103,000 grimoires. She's constantly being targeted and he ends up being the only one that can help her. He doesn't have any abilities of his own thanks to his right arm that cancels out magic effects.
~ Index and Railgun are perhaps two of my favorite animes. They're both in my top four, anyway. In a world of espers and magicians and apparent constant danger, Touma's right hand cancels anything. It's so much fun to watch him go around and punch things, I swear.To Aru Majutsu no Index II - Season 2 (3 kind of) of above.
~ Yep!To Kagaku no Railgun - Side story of Index that aired after the first season. You'll want to watch this before the second season.
~ Personally I watched Railgun before either of the Index ones (partly by accident since I didn't know it was a spin-off) but that's okay because in my mind there are plot points that mean Railgun comes first chronologically, and I like Railgun better than Index (well, sorta. Accelerator (Index character) is awesome. Hmm...)