See below for today. I had posts doubling.
Does this happen when you switch to another theme.
If it doesn't show up in another theme, then (I think) the problem may be in the index file of your theme.
Look for and identify The_LOOP. If you don't know what it is, see the Codex.
Then look for anything within The_LOOP that occurs more than once. To check, use comments;
<!-- before what looks like something extra, and
--> after just that line.
Then hit the button to update your code, and hit the <view site>.
If that worked, you should be seeing either single or double. If single, then you are fine. If you are seeing double, there might be another extra line of code in The_LOOP (particularly "content" lines in PHP code).
If those things don't work, then MichaelH has the right suggestion, about plugins.
To troubleshoot plugins, take them one by one.
Deactivate the plugin
<view site> if your blog is still in quadruplicate.
If it is, reactivate the plugin.
Repeat until you either find the plugin that is causing problems and deactivate it, or you run out of plugins.
Just in case it's more than one plugin, note where you stopped.