Just check this list to see if I watch anime or not
I tend to watch anime that come from certain anime companies like Sunrise, Kyoto Animation, Madhouse, Production IG, and Bones. Usually these companies produce the best anime series out there, but they do tend to release mediocre ones once in a while. I generally like watching action (Gundam) and romance or slice of life (CLANNAD) shows. They tend to have more plot and character development than a lot of American TV shows. I also watch moe and comedy shows (Lucky Star and K-on!) because most of them are funny, not because they make me want to scream KAWAIIII into my laptop and "make *insert female lead here* my waifu" which gives a very negative impression of people who like watching anime.
As for anime I don't watch, I don't watch Naruto, Bleach, One Piece, or any anime that runs longer than 50 episodes (except maybe Fullmetal Alchemist). They have no conclusion, a battle takes 2-10 episodes long just to charge up, and they're the epitome of cliches and unstable power levels (Super Saiyan 1, 2, 3, 4, fusion, shikai, bankai, hollow masks and all that).
Just ranting here, to people who say anime is kiddy, go watch Death Note or the Higurashi series, and tell me after watching those shows you still think it's kiddy. To people who say anime is boring, a lot of times you might have just watched a poor example of a good anime, so it's not entirely your fault that you think it's boring. To each his own though, I can't say I'm interested with shows like 24, Lost or Heroes.
EDIT: Forgot to put favorite shows!
Favorite shows that are done:
CLANNAD, Gundam 00, Bakemonogatari, Higurashi series, Lucky Star
Favorite shows that are currently airing:
To Aru Kagaku no Railgun, Kimi ni Todoke, Kobato.