Yeah, but
As for tastes genre-wise.. I don't think I really have any tastes? I think the animes I watched aren't many.. Some Bleach and Naruto (never finished either due to the huge amount of episodes for both), Death Note, Code Geass, Elfen Lied, Erementar Gerad, SAO, Accel World... and apart from some old ones, I guess that's pretty much it. ^^'
(I do dislike animes that have quite some episodes, anything over 100 just seems extremely boring and long for me.)
I know that feeling. I watched nothing over the 60 episodes. If I want to watch something but it is too long, I usually choose the manga. This way I read Naruto, Dragonball (which I watched on TV, though), Detective Conan (in a couple of day I'll have finished this)
As for some anime you may like, since you don't have a favourite genre and the anime you watched are pretty different one another, I may only try and suggest you some "mastepieces". I'd suggest you a couple of really short anime, about 13 episodes, because they're the ones I like the better. I'd say, this short:
Angel Beats, pretty nice, I didn't cry, but it is the anime which shed more manly tears ever, probably. It's quite funny, expecially when you start to know TK.
Ano hi mita hana no namae bokutachi wa mada shiranai, aka Ano Hana. Awesome anime, really. I usually suggest this to anyone, no matter the genre. I never heard anyone talking bad about this.
Another, pretty creepy, but really awesome. I myself like both the MCs. I cannot talk about the most interesting facts because it'd be spoilerous.
Black Lagoon, I liked it, not too much, but I cannot say it was bad, not at all. Pretty entertaining and stuff, but I heard lots of persons talking awesomely about it.
Mahou Shoujo Madoka Magica, damn it, it is just too awesome. No more talking.
Suzumiya Haruhi no Yuutsu, awesome, most likely better than Madoka, too.
Those were the Masterpieces, but other short anime may be:
Arakawa under the Bridge, it is a comedy, 13-episodes long, but has a second season of other 13 episodes. Pretty funny, for sure, but it won't be at the levels of:
Baka to test to Shoukanjuu, funnier than Arakawa, and has some neat characters. This one, too, has two seasons of 13 episodes.
C - The Money of Soul and Possibility Control. I discovered this one by luck, and no friends of mine have watched it, but it is really an awesome Seinen, and probably the only one who talks about something like that. It applies money to battle in a really incredible way. Definitely suggested.
Denpa Onna to Seishun Otoko, funny with romance, a good combination. I don't usually suggest this when going for something random, but if the person I'm suggesting stuff likes romance, well, this is one of the first candidates.
For other suggestions, take a look at my list:
http://myanimelist.net/animelist/Leodip