I bought some pepper plants at a nursery this year - Red Bell, Marconi, Jalapeno, and Hot Banana. As these were bought at a nursery, would I be able to save the seeds and plant them next year? And if so, do I just rinse them and dry them?
You can with a "but"...
Peppers will cross pollinate to some degree, and the hot peppers are dominate so you can wind up with hot peppers that look like sweet peppers. This article has good info on separation distances for home gardeners (though they still require a lot of distance!):
It could be a fun experiment, or you may just want to purchase seed for next year to make sure you know what you're getting. This article has good info on saving the seeds: http://faq.gardenweb.com/faq/lists/seedsave/2002084357025280.html