Q: Can my 3rd generation itouch do apps?

Yes. A 3G can go as high as iOS 5.1.1. However, some users think they have 3G when they really have a 2G. A 2G can only go to 4.2.1

Identifying iPod models

iPod touch (3rd generation)

iPod touch (3rd generation) features a 3.5-inch (diagonal) widescreen multi-touch display and 32 GB or 64 GB flash drive. You can browse the web with Safari and watch YouTube videos with Wi-Fi. You can also search, preview, and buy songs from the iTunes Wi-Fi Music Store on iPod touch.

The iPod touch (3rd generation) can be distinguished from iPod touch (2nd generation) by looking at the back of the device. In the text below the engraving, look for the model number. iPod touch (2nd generation) is model A1288, and iPod touch (3rd generation) is model A1318.

An A1213 is a 1G. Those can go as high as 3.1.3 you get here:

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

There are still some apps compatible with 3,1,3

VintApps 3.1.3 for iPhone, iPod touch, and iPad on the iTunes App Store

apps for ios 4.2.1: Apple Support Communities

Finding iOS 4.2.1 Apps Compatible with Older Devices - Apple Club

HT4972 Touch Game 4.2.1 Apps: Apple Support Communities

apps for 4.2.1 (also works for 3.1.3)