Ugh, putting the words "realistic" and "romance" together in any TV show, anime or not, pretty much narrows the playing field to almost nothing.
Erm, yeah. Honey and Clover is a good bet; it tries to be funny (and succeeds IMO), but the characters there are quite three-dimensional and not just the stereotypical Kimagure Orange Road spinoff. Bokura no Ita is also a pretty real and effective portrayal, though it focuses more on the aftermaths of a relationship rather than the relationship itself. SaiKano is entirely serious, mature, and cheese-free, though its situation may be a bit too idealized for you to enjoy. Ashiteruze Baby has a slightly different focus than love - that of a former playboy brother suddenly having to deal with the responsibility of taking care of a child - though there are romantic, well-portrayed elements within the show. Koi Kaze is real almost to a fault; it's about a incestrous relationship between a grown man and a sixteen-year old daughter, though it's one of the most realistic and accurate anime I've seen in a while. Hanbun no Tsuki ga Noboru Sora and Spice and Wolf are what you'd call entirely serious anime, though the romance is not actively portrayed and only hinted by the progressively friendly relationship between the male and female leads. The melodrama series mentioned earlier (and Rumbling Hearts) are okay if you're into that kind of excessive drama, and - er, I don't think I have anything else to add.
Also, never watch the last episode of School Days. You will never watch another anime again if you do so.