Reputation points is one of the key innovations of Stack Overflow. If you took it off, then the resulting site would be pretty similar to a traditional forum, I think.
One of the key elements of Stack Overflow is that when you post a question, you get an answer very quickly. I believe this is because of reputation points, and the incentives to increase your reputation points by posting an answer.
If reputation points were taken off the site, people would still answer questions.... just not nearly as quickly. So in that sense, the nature of the site would change - from a site where you can ask a quick question and get a quick answer in realtime, to a site where you can ask a question and wait a few days for an answer or two (if you're lucky).