Aishiteru to Ikketure - this is by far one of the most satisfyingly romantic Japanese shows I've ever seen. The first 9 episodes are absolutely beautiful, then the writer(s) smoked crack & f'ed the last 3, but still absolutely worth the watch!
Orange Days - a great watch & a really sweet romance!
Brother Beat - family drama with lots of bromance and romance. And lots of LAUGHS. I loved this show the first time I saw it!
Also ...
Pride
Rich Man, Poor Woman
Mahiru no Tsuki - about a woman suffering from ptsd after being raped, and the stress her situation puts on her once happy relationship. Deals with a heavy topic, but I didn't find it too heavy to watch.
Ice World - a police detective investigates a mysterious woman's involvement in a series of baffling crimes. Doesn't sound like much of a romance, but it is.