Like the earlier poster - What don't I watch? I have Anime Friday at my house every Friday night, so we see a lot of stuff.
One anime that I didn't see mentioned is
Zettai Karen Children. If you like comedy that also makes fun of other animes (lots of parodies) then this is for you. It also has
Hayate the Combat Butler making a few guest appearances. The last episode (#46) was a
Death Note parody that had me holding my sides (I pulled a muscle I was laughing so hard). Definitely give it a look. The first episode is not a very good reperesentation of the whole. Watch five episodes, then decide if you want to continue. Another show that had a great
Lucky Star parody episode in it was
Kannagi. I liked this show, but the ending of the first season is a cliffhanger. I hate that!
I agree with everyone who already mentioned
Toradora. This show is one of the best out there. 10 out of 5 stars.
For pure zany antics watch
Kemeko Deluxe. It is like
FLCL or
Excel Saga. Pure insanity from beginning to end. Another good one is
Ninja Nonsense.
For good action and story
RideBack is pretty popular right now. I just wish it came out faster. Another popular action anime is
Regios, it is sort of like
Scryed If you liked that show then give
Regios a try.
For those who want a Shōjo fix then watch
Saiunkoku Monogatari. This show is the best period drama I have ever seen. Loads of fun. Guys will like this one as well if they give it a try. You might even get your parents to watch this one with you. It really does grab you.
My list is mainly shows that are current, believe me I can give you a much longer list if you want all the shows I like.
As was already mentioned the best magical girl show is
Nanoha. It is obvious that the first season is stealing a lot from
CardCaptor Sakura, but I think it actully is better than that show in some ways. The second season
Nanoha A's has the heroine growing up quite a bit and the story arc is a little darker. The last season
StikerS has Nanoha as an adult instructor teaching young mages. It is more mature than either of the previous two.
If you want an anime that is beautiful to look at and has a decent storyline then check out
Moribito - Guardian of the Sacred Spirit. This anime started on Adult Swim, but I guess has been dropped. A real shame because the show is AWESOME! The animation is Ghibli quality throughout the entire series. A true masterpiece.