- Anything by Adachi Mitsuru. He mostly does high school sports stories with a romantic interest.
- Living Game is a comedy about a guy who's trying to find a better apartment. At least, that's how it starts.
- Yotsubato! is a series of adventures of a wide-eyed, cheerful little girl (5 years old?) discovering the world. Extremely cute.
- Hikaru No Go is about a young boy who meets the ghost of an ancient go player, and learns the game. You wouldn't think a story about a board game would be so interesting. The anime version is also excellent.
Other than Yotsubato!, which doesn't have much in the way of continuity anyways, these are all completed, so no getting to the end and then having to wait a month for the next chapter. Things like Death Note and Full Metal Alchemist don't get a mention; I assume you know about them already.