I'll try to focus on recent series since animation seems important to you:
Honey and Clover while this is more about the journey than the actual romantic relationships I still consider this the gold standard of slice of life romantic series. My all time favorite anime.
I'll second Tonari no Kaibutsu-kun and Kimi Ni Todoke, although most of the time where they actually spend as a couple comes after the anime finishes in the manga.
If this is the genre you like (it's also my favorite genre) I think you'll find more series you like with manga instead of anime, if you enjoy manga as well I'd recommend highly
Horimiya,
Bonnouji and
14-sai no Koi