From The Apple Wiki

iPhone OS

iPhone OS Jailbreak Tool Tool Version Device
iPhone iPhone 3G iPod touch iPod touch (2nd generation)
2.0 PwnageTool 2.0-2.0.3 Yes
QuickPwn RC3-2.2.5 Yes No Yes
2.0.1 PwnageTool 2.0.2-2.0.3 Yes
QuickPwn RC3-2.2.5 Yes No Yes
2.0.2 PwnageTool 2.0.3 Yes
QuickPwn RC3-2.2.5 Yes No Yes
2.1 PwnageTool 2.1-2.2.5 Yes
QuickPwn 2.1-2.2.5 Yes No Yes
2.1.1 redsn0w Lite Tethered[2.x 1]
2.2 PwnageTool 2.2-2.2.5 Yes No
QuickPwn 2.2-2.2.5 Yes No Yes No
2.2.1 PwnageTool 2.2.1-2.2.5 Yes No
QuickPwn 2.2.1-2.2.5 Yes No Yes No
redsn0w 0.3 No Yes
  1. ^ Tethered for devices running the old bootrom only. Will not work for devices on the new bootrom (new bootrom devices cannot run iPhoneOS 2, only 3).