I'm honestly not a huge Shakespeare person. As someone who majored in lit, I kind of thought "oh god, not another one" when I encountered a student or professor who was a self-proclaimed Shakespeare buff.
I also think that Jane Austen is overblown in a similar manner. It can get on my nerves, but it's just my personal thing. The way some people talk about Jane Austen you'd think they didn't know other books existed from that time period.
Anyway, when it comes to Shakespeare I prefer his sonnets, and I guess Hamlet is probably his best play, IMO. I don't think people committing suicide for love is romantic, especially when they're only teenagers, but taken in the context of the historical situation, Shakespeare was actually making a very good point...you have to look at the broader historical context and the social commentary he was making rather than the love story, if you want a mature understanding of the play, in order to appreciate why it's timeless.