Do you mean your old blogs? Or old blogs you follow?

For your old blogs; Click on the tumblog of your chosen blog, click 'Settings', scroll down and click 'Delete this Blog'....

For old blogs that you follow;

• Go to your dashboard, then click on the box where it tells you how many blogs you follow, as you scroll down, the blogs that have been deleted will have their URL, followed by DEL and a sequence of numbers... for example 'oldblogs+DEL647658'
• Under each blog name it will tell you when they were last updated, so you can judge for yourself which ones you wish to un-follow (: