Yes
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The Sims 3 is not free, but there are apps like Shazam, Facebook, TweetDeck, and some games and other apps that are.
Apps can be removed at any time, but all apps that are on the iPod Touch will remain there unless you delete them.
These are the some apps like juxtaposer COLOR SPLASH, ADOBE LIGHTROOM FOR IPAD, LIGHTLEAP BY LIGHTRICKS, SUPERIMPOSE
You can pay if you want to be able to watch episode sooner and some series. I use my iPod crunchyroll app and it hasn't costed me anything so far.
There is a big difference between apps and games. Games are always for fun or for educating user. Apps can be about any thing, apps are not always about entertainment or for education people. Apps can be about professional stuff, sports, fun, information, short cuts etc.