I have a website very similar to this that I made from scratch. It's called www.Citybeams.com. I already have decent Google search engine results for a good amount of keywords and question titles. "City Questions" and "City Answers" page one Google for example. I was thinking of moving the whole site to a Pligg.com template still under the same domain am I'm wondering if that could hurt my search engine results?
It depends. If the site is going to be exactly the same, just using a different domain name, and you use 301 redirects to redirect from the old UTLs to the new URLs, then you'll be fine. You probably will experience a slight "hiccup" while the search engines sort everything out, but in the end you should be fine.
If you are changing the HTML and internal linking structure of the website in addition to using a new domain name, then you do risk losing your rankings. There are many factors in determining a page's rank and the changes you make may have a negative effect on your rankings. Nobody can say for sure because it would require an extensive review of the code and the internal linking structure of the old and new site just to get an idea of how different they are and if change seems to be for the better or worse.
If you rank well for search terms that drive good traffic to your website, then making a change can be considered a bad risk to take. However, if making this change can mean more success for you in other ways then it may be worth the while.