There might be reasons why you want to keep your Tumblr account but delete all your posts. Perhaps you land-grabbed an awesome Tumblr username or URL and you don't want to give it up, but you'd rather people not know about how into anime GIFs you once were, your dark obsession with Henry Cavill, or how often you post about cats during the 9-5 work week. Things like that.
Tumblr offers a Mass Post Editor, which you can use to add or edit tags for a bunch of posts at once or delete the posts entirely. However, if you've been Tumbling (Tumblring?) for some time, this is going to be an arduous process, seeing as you have to click every single post individually before performing a mass-delete.
And, no, clicking one post and shift-clicking another post to quickly select a group doesn't work. Good idea, though.
Thankfully, there's a little trick you can use to select batches of 100 posts at once, and you can continue to repeat that process — selecting, deleting, selecting more, deleting more, et cetera — until you've cleared out your Tumblr for good. Yes, this will still take a little time if you have thousands of posts, but it's a lot better than clicking each one individually, at least.
Confession: I already deleted all my old Tumblr posts before taking a screenshot. Just pretend this, times two thousand, is what your Tumblr looks like.
Yes, I have a lot of old bookmarks I have to go through.