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