My thoughts:
1. The best classic romantic comedy is L.A. Story. By "classic," I mean that both main characters are generally likeable and the obstacles to their relationship bliss are largely external. This one is Steve Martin's best movie, and bonus points for launching Sarah Jessica Parker. It's the perfect Steve Martin mix of high-brow and low-brow, except the high-brow is more prominent and that's good because I think Steve Martin is better at it (though it could just be my preference). Anyway, I've seen it a lot of times and I still laugh.
2. The best romantic comedy screenplay is As Good As It Gets. That's one of the best screenplays ever. It is so well-written from top to bottom. It's not a classic romantic comedy, in that the main obstacles to the characters getting together is that one of them is a complete ass, but it's still hilarious, crisp at all times, and has a wide emotional range.
3. Steve Martin's second best film is also a worthy romantic comedy: Roxanne. That one has some great gag scenes, and is also quite clever. It's telling that Roxanne is (very loosely) based on Cyrano de Bergerac, and LA story (very very loosely) on Shakespeare. The high-culture references anchor the films in something deeper, which is important for rom-coms because the genre gravitates to silly shallowness.
4. I've only seen Shakespeare in Love once, and it was a long time ago, and I was pretty tired and don't remember it well. But I do remember being impressed with it when I watched it.
5. I like the movie Big Fat Greek Wedding. I think it's very funny. Mileage on it might vary, though. Not sure I'd call it a great film or a great screenplay, but I always liked it.