Android - Can I re-install a purchased app from Google's Play Store?

You can uninstall it and the market will remember that you bought it. It'll say "purchased" in the market and you can reinstall any time. Every time I reflash a ROM I go into my downloads section of the market and I see all my purchased apps.

Procedure for most Android phones is: Open the "Market" application, click your phone's Menu button, click "Downloads" or "My Downloads", click name of App that you previously purchased, click Install button.

Note: If you've also changed the Google Account associated with the phone, then you'll lose the ability to install apps purchased under the old account.