Bokura ga ita (this is one of my favorites! really good)
chobits (really cute)
Dears(reminded me of a more ecchi version of chobits, I liked chobits a lot but Dears was just ok.)
Paradise kiss (funny but romantic as well)
Air (this is one of the best romances ever! Pure, honest, sad, one of a kind)
Honey and Clover (both seasons are OMG! there were parts I just couldn't stop crying)
Myself;Yourself (really touching, I loved the part with the twins -I won't say anything more I don't want to spoil it-)
Kamisama Kazoku (funny, fast moving and lovey dovey situation between an angel and the son of god
)
Ef-a tale of memories/Ef -a tale of melodies (the second season is now airing)
Hanbun no tsuki ga noboru sora (this was awesome. only 6 episodes but awesome)
Ginban Kaleidoscope (this is a bit weird and childish in some way but I liked it)
Touka Gettan (26 episodes, you watch it backwards. you start from episode 26 and end at episode 1. I loved that anime)
Kyoshiro to towa no sora (I think it's considered mecha not sure. Very good)
Lamune (a touching story about 2 childhood friends)
True tears (really good)
If you are also interested in anime movies that include romance you can watch:
Howl's moving castle
5 centimeters per second
The place promised in our early days
Whisper of the Heart
those come in mind right now that weren't mentioned...