When it comes to favourite anime.. it's so many good animes that it's hard to just pick out a few, so it all depends on what kind of animes you like or dislike. Just to mention a few of those I first watched when I started to watch anime.
Death note, also one of the first I checked out, and I enjoyed it, one of the most viewed animes out there I guess.
Azumanga Daioh when I started watched this anime, I had to ask myself "wtf am I watching?". But after a few more episodes I was pretty much addicted and watched it till the end, enjoyed it overall.(You might not like it if you dislike Slice of Life animes)
Toradora Don't have much to say, I enjoyed it. :>