Wow, I haven't felt this depressed since I finished Philip Pullman's Dark Materials trilogy. Good job, Sola.
Anyway, about me...
Let's see, I like shows with plenty of romance in them, though it doesn't necessarily have to be the central theme. The shows which get put at the very top of my list are usually the ones with a bit of romantic development and lots of heartwarming moments. I recently came across the concept of 'nakige', and this probably sums up what I enjoy most in the shows I watch.
Air was the first show which really got me into anime, followed by Maburaho and then Myself;Yourself. Although I've seen plenty of shows since the latter, it will always hold a special place in my heart - I must've watched it about ten times that first summer I found out about it.
My absolute favorite studio would be Key. They've produced really high quality shows, and really understand the tear-jerking themes of romance, memory and death.
I gotta stop watching romance anime, my ship never wins and someone else gets hurt.