no you dont, but for some reason, when i tried to redownload UNO, it is asking me to purchase again. WTF? I bought it for 99 cents when it came out. trying to steal my moneyz.
You can also login with your live account here: Windows Phone Apps+Games Store (United States); this will allow you to track your purchase history if you need to re-download an app/game in the future.
There have been temporary bugs in the store where users were charged a second time for the same app, when attempting reinstall, but if you have, and you contact Microsoft through the store (I'm guessing there's a link in the store on the web page), I've heard that they've been helpful.