I have apps I paid for 3 years ago on my current phone (4th since I joined Android) and they are also on my tablet and my wifes phone (I added my account on there)
you can uninstall and reinstall as you wish (as long as it's not pulled from the market), when you find the app in the market instead of a price it just says "purchased" (or it will also always be at the bottom your "my apps" list when not installed)