I was just wondering if there is anyone else that has never burped, and if this is a bad thing? The only time I came anywhere close to burping, was when I was vomiting. I have only vomited 3 times in my life. One of these times was from drinking too much Jaagermeister on New Year's Eve. Would the lack of burping and vomiting be linked to each other?

I don't think they are directly linked to each other.
Burping is caused from trapped air.
Gas, Bloating, and Burping (http://www.ghc.org/kbase/entireTopic.jhtml?docId=gas)