First of all, let’s make an important difference between an account and a Tumblelog. If you want to delete a secondary/alternate Tumblelog, here is how to do it.  Now, if you really mean deleting your account, then you just have to visit this link, enter your password and that’s it, you will automatically be gone from  Tumblr.

This is the only way you can delete your main blog from Tumblr.  However, you could also delete all your posts and change your tumblelog’s url name, but you would still have all your followers, and you can’t get rid of them.  Also take into account that after deleting your Tumblr account, and if you had an additional blog that had another member besides you, that Tumblelog will still be up and running, since there’s not an administrator option to regulate that.