I've been battling this for quite some time now and can't figure it out. I thought it was related to magic quotes. I have been able to successfully disable magic quotes and have verified that they are indeed set to off. Which did fix the slashes being entered into hyperlinks.
However, they are still appearing before apostrophes. For example, "what's" becomes "what\'s". This wasn't too big of a deal until recently. I have added a new feature to my site and have been adding more text content. So now there are more words with apostrophes, it's very apparent that something is wrong.
I found an old post on here, but unfortunately the page with the "fix" on it is no longer available and they never posted the fix within the post for some reason. http://wordpress.org/support/topic/slashes-appearing-before-apostrophes
Any help would be greatly appreciated!