This a a very common problem so although Chuck has written about it here: Warning: Do not delete your blog (close new window/tab to get back to this page), I think that by writing another post of the insidious problem, more people will (and should) know about it.
If your blog has been on the Web for some time, it probably has been indexed by search engines and have a non-zero PageRank. See What is PageRank and how you can easily get it (close new window/tab to get back to this page). So your URL has value to spammers. They will grab the URL for their spamming purposes when you make it available by deleting it, by changing the URL or by changing to hosting it on your own domain via FTP. Some even use it for putting porn on it. This can be very embarrassing for you if you have been giving the URL to your family, relatives, friends, colleague, etc.
What you should do when you don't want your blog on the Web anymore is to delete all your posts and then wait for the cached copies of your blog to disappear from the Web (this may take some time). If you change the URL of your blog, you should immediately try to claim it back, and if you succeed, do a redirect to your new URL. Look at this post on how to do a redirect: How to redirect from old URL to new URL (close new window/tab to get back to this page). That is for blogs using old classic Blogger template. If you are using New Blogger template, refer to Redirecting New Blogger blog to another site (click BACK button to get back to this page).
Chuck mentioned making a "stub" post (which he described as a post of no value. something like "This blog has been moved" or something like that), but I think all that is necessary is to delete all the posts. If you do make the "stub" post, I suggest you remove your profile.
If after reading this post you still want to delete your blog, this is the way to do it.
Sign into Dashboard
Select the blog
Click the SETTINGS > BASIC tabs
Right at the bottom of the page, click "Delete This Blog"
Then don't blame me if you see unpleasant stuff at your old blog address.
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