Mine are the following:
Bleach - This is actually what got me into reading manga. I had always been exclusively anime prior to that (since i was a child actually, if you remember Unico).
Naruto- This anime was what spring boarded me into Bleach. Imagine that. I was downloading episodes of this and ended up coming into Bleach anime, which led me to start reading the manga. Been on it ever since. Kind of owe Naruto credit for this. Then i picked up the Manga for Naruto and read till the end.
The Breaker - This is a Manwa. This storyline is on par with any of the manga's i have read over the years and remains interesting. It's currently on hiatus but should be returning shortly. The characters are well developed and the storyline is pretty much thoroughly explained.
Claymore - I watched the anime first, but the anime was not nearly as good as the manga. The manga was every bit worth the read. Great cast of characters, great story, excellent ending.
Umineko Naku No Koro Ni - Picked this up somehow. Don't remember how. I just know the story is long and impressive and fun to read. It started as a video game in Japan, i believe.
Chrono Crusade - I thought this manga was good and always had some form of comic relief. Enjoyable story.
I have not read as many as most of the users on here. I plan to take up another one. I was considering starting Saint Seiya, but i am not a fan of the art work. That said, i may still read it anyway. I would have mentioned One Piece, but i couldn't continue with it when they were on that toy island. I lost interest in it. I may resume it soon. Fairy Tale is the same. Great start to the story, but got boring after a bit.