Reading

This list is neither all-inclusive nor static. I'll add to it. If you have suggestions, please let me know. Starred entries are pay sites (full or partial) that I think are well worth the money.

News 

*Buster Olney
ESPN
Gammons Daily
Grantland
Hardball Talk
MLB.com
Ken Rosenthal

Analysis

Baseball Nation
*Baseball Prospectus
Beyond the Box Score
*Bill James Online
Bleacher Report
ESPN SweetSpot
Fangraphs
Hardball Times
*Joe Sheehan
Just a Bit Outside

Numbers

*Baseball Prospectus
Baseball Reference (including the astounding *Play Index)
Baseball Savant
Brooks Baseball
Fangraphs

Team Blogs

I am going to list just a few favorites. There are a lot of very good ones, easy to find.
Aaron Gleeman (Twins and lots more)
Rockies Zingers (Rockies)
The Captain's Blog (Yankees)