Not a manga expert here at all, but I've been told the manga for Umineko no Naku Koro Ni is pretty damn good.
I watched the anime adaptation, and... here's the nicest way I can put it: the opening was better than the anime itself. It focuses around a mystery and never solves it, which makes the whole story pointless.
The manga, however, is complete, and since I'm too lazy and have no time to read manga in general and umineko is not getting continued at this point, I decided to look up the mystery myself and find out about the things that remained unexplained in the anime and, my god... that was truly amazing. Not only that, but the way you find out about it, the whole journey of reading it makes it seem like it would've amused me a lot.
Also, try out To Aru Majutsu no Index, if you're more into action or sci-fi. That's the only manga I've ever read (or tried to, at least) and from the little I read, it was great. It's huge (about 20 volumes iirc) and there are a lot of characters, but if you have the time, I'm sure you'll enjoy it a lot.