I'm not actually much of a Drama fan but there was a period of time where I wanted to see what the hype was with dramas.
However the one's I usually watched by myself were the ones in the mystery/detective/crime genre such as...
The Brain (or something...can't remember the title)
They were pretty good.
OH There was this Korean Drama which I absolutely fell in love in
I also happened to go to a friend's home while she was watching
1 Litre of Tears
and ended up watching with her.
God that made me cry so much (how embarrassing)
I don't think I'll ever be crazy about dramas but I'm definitely not averse to them either. My mum is a huge fan of dramas though.