I'll be a little selfish here since you're sort of asking for *my* favorite romance anime.
Kimi ga Nozomu Eien: Excellent anime that sidesteps the highschool romance cliché. While the relationships starts in high school, it goes beyond that. It has a general theme of "friendship" which I though is very cool.
ef - a tale of memories: Masterpiece. Make sure to watch its sequel,
ef - a tale of melodies.
Itazura na Kiss: I love this anime for its completeness. Half of the anime is about how the relationship starts until the couple gets together. Usually this is where most anime stops, but it further explores the romance by following those characters to college then into their professional careers. Despite its few flaws, it is overall probably my most nostalgic romance anime.
REC: This anime follows the life of a 20-year-old female protagonist who aspires to be a seiyuu. It's an excellent watch it you want a dose of realism--at least more realistic than typical highschool romance.
Hanbun no Tsuki ga Noboru Sora: Hospital romance anyone? It's actually somewhat funny for the serious atmosphere, but the 6 episode OVA is quite satisfying.
Hotarubi no Mori e: Beautiful. It's a slow-paced slice of life movie that I can't say more about because it will spoil you.
Acchi Kochi: If you're not into slice of life, then don't watch it. However, I'm also not into slice of life but I found this a nice watch. The innocent relationship between our two protagonists are just too cute to resist.