I am writing this so Google can index it. I have been asked this several times and there is a good way to tell using free tools and a general rule.
WHAT IPHONE AND IPOD MODELS CANNOT BE JAILBROKEN?
Can my iPhone or iPod Touch be jailbroken or dos it require tethering?
Generally speaking, all iPhone 3g and older models can be jailbroken.
The same can be said for the iPod Touch up to second generation.
ANTI PIRACY BY APPLE:
After the release of the iPhone 3gs, Apple started to put a different type of memory (RAM) in the iPhone and iPod touch. This memory prevents the device from staying in an always jailbroken state.
Each time the device restarts either due to a user restarting it or a complete battery drain, it must be connected to a computer and you must run blackra1n to rejailbreak. Even though this takes only a few moments to do it is a major hassle if you do not have access to a pc.
NO MORE PROBLEMS, HERE ARE SOLUTIONS:
For those of you who want to know whether or not your iPhone or iPod is good to jailbreak, there is a quick rule of thumb. If your device has a model number starting with MB you are likely fine.
For those of you with an MC model chances are you are destined to tether your jailbreak.
Another sign can be found five characters into your serial number, this indicates the week your iPhone was manufactured during the year. The lower the better if your iPhone was sold In 2009 as after week 42 almost all iPhone and iPods were made with the new anti-piracy memory chips:
An even better solution recently launched is the free tool called F0RECAST which will query your device to see what can be done with it. You can download the f0recast tool here