No. You download games to your Wii HD or a SD Card. Games are locked onto your console. That means that they will only work on yours. You can take them and put them on an SD cards for backup purposes, but it won't work on another person's Wii. Also, the online store allows you downloads for life. If you accidently delete the game, then you can download it again whenever you want.
PS: Welcome to the forum!