can an old iphone 3 be used just for games?

If the phone is deactivated then you need one to activate it, but it does not need to have an active service plan attached, it just needs to be a valid sim from the carrier the phone is locked to. Heck if you have one that fits from another phone with the same carrier it should work to activate it, and you can then take it out.

Other than that you can use the phone without a sim card just fine if its already activated, or after you manage to activate it.

An active/new SIM is not necessary to use the device like an iPod. See this support document for some help in doing that. http://support.apple.com/kb/HT3406

Is it an iPhone 3G or 3Gs?

If you have any SIM that fits properly, you can use that to activate it in iTunes, then use the device effectively as an iPod touch. Once activated, you can remove the SIM, so you can even borrow one if possible long enough to activate.

However, your problem will likely come about from iOS. A 3G can only run up to iOS 4.2.1, while a 3Gs can run iOS 6.1.3. It will be harder to find games that run on iOS 4.2.1 then 6.1.3 - but other than that (finding compatible apps to run), you can certainly use any iPhone without a cellular service plan at all.

Well, no that will not work. An iPhone 5c uses a nano-SIM and you need a regular sized SIM for an iPhone 3G or 3Gs. But any regular size SIM you can get hold of long enough to activate it in iTunes will be fine.

Was the SIM card that is in the phone your old number that you are using now in the newer phone? If so, then it won't activate cell service, but it will be sufficient to activate the phone. If you wiped the phone and then restored it,then you would have to sync apps back over from iTunes, but as mentioned earlier, if apps on the newer phone are for an iOS that is newer than iOS 4.2.1, which is the latest you can run on the 3G, then they will not work.

Well first off, the SIM only needs to be in there for the activation process. Once you can get into the phone, you can remove it, but it is non-functioning at this time so there is no reason to remove it. Also, if you have to restore the phone at some time, it will still be there for the activation process.

When you went to sync, did you have apps selected to sync in iTunes? Also you are correct about apps that will not run, would not be downloaded. The only place to get apps is the app store. There are some places where you can search for apps that support that iOS, but developers are retiring apps that support the older iOS. The iPhone 3 was released back in 2008, so in technology years, it is ancient.

Where is the original SIM card for that phone? If it is still in it, that would work.

I would just borrow a sim card from anyone that has a phone that uses a regular sized sim card. As Chris points out, if the orignal sim card is still in the phone you can activate using that.

You're welcome.