Does playing games on the iPhone take up data usage?

I just got an iPhone 4, and I was wondering if playing games such as 4 Pics 1 Word, Wordsearch, Mahjong, or Chess would take up data? I'm connected to my Wi-Fi, if that's important. I only have 2GB a month, and I can't afford to go over. Thanks.

Added (1). My carrier is Verizon.

I would just turn off your internet and use your Wi-Fi while at home. That way you know for sure you are not using up all your data when you do not want to.

There's no doubt that online graphics, heavy multi-player games use up a lot of data fast. Even those simple games like angry birds or those free games you mentioned uses data, this is because many of the free versions of games for mobile devices are ad supported. These ads get to your phone over your data connection.

If you're connected to Wi-Fi, you're not using data.

Any game that requires internet access & done so over 3G/4G will use data. If on Wi-Fi, none at all.