Do iPhone games really take up Internet connection?

[942]

Lately, I've decided to start playing games on my iPhone (Jetpack Joyride, Temple Run, etc). A friend of mine told me that games (in general) take up Internet Connection and if I play when I'm not hooked to Wi-Fi, it'll send the Internet Connection used to my monthly bill (I don't have an unlimited Internet plan, so it might be a problem). So do normal games that (apparently) don't have any Internet Connection also take up Internet from my phone or does that only happen in games that actually use Internet, like "The Simpsons: Tapped Out?"

[Bone Alone]

Some games require Internet connection to play, while others don't.

I believe Simpsons need Internet to play.