In Android, every app has his own "sandbox". This is like a exclusive folder for the app, where it stores everything and other apps can't access.
When you remove an app from the phone, android removes this "folder" so there is nothing left behind.
There is just one exception to this: the SD card. Some programs will store some information (for example heavy games store maps, voices,...) to a folder in the SD card. So when uninstalling just look if your SD card contains some folder with the app name and safely remove it too (unless you plan reinstalling the app later!).