Some blogs I follow:
Scott Aronson's blog
Gowers's Weblog
Combinatorics and more (Gil Kalai)
Gödel's Lost Letter and P=NP (Richard Lipton)
Igor Pak's blog
Windows On Theory
What's new (Terence Tao)
In theory (Luca Trevisan)
Yufei Zhao's blog
Zeros and Ones