When I first started researching this it appeared the iPhone and iPod Touch might not be able to run multiple processes, but I was starting to wonder how in the world could that be. This does not appear to be the case though and instead it appears that Apple has set forth some fairly strict guidelines to keep developers from developing applications that eat up tons of RAM by allowing them to run wild with background processes. The iPhone has 128MB of RAM thus it could be chopped down to nothing very quickly by multiple applications running at the same time.
So obviously the iPhone can run multiple processes because you can be surfing the web and your phone could ring at the same time. The articles I read stated that the iPhone and Touch are based off of the same BSD and Mach that OSX is. A lot of people are probably familiar with BSD, which is a UNIX OS, but some may not be familiar with Mach. Apples web site states that Mach provides memory management, thread control, hardware abstraction, and interprocess communication.
Anyhow one of the articles I read was talking about there is no reason that multiple applications cannot run at the same because the iPhone is a first class UNIX system. The articlethen goes on to make a case to jailbreak the phone to gain access to an application called backgrounder. I agree the iPhone is a first class UNIX system and the fact that it is a first class device all the way around. I however also agree that Apple is making the right choice making developers adhere to a set of rules during development of third party applications thus keeping things first class all the way around. The device only has 128MB of RAM and allowing developers to run wild with background processes could easily jeopardize the stability of the device in my opinion. So there is always the case to jailbreak the phone which definitely has positives though so far for me they do not out weight the negatives at this point.
At this point if you want to run multiple applications at the same time you would be required to jailbreak your iPhone or your iPod Touch. I personally can live with one application at a time for now with my Touch as I prefer the speed and swift functionality versus multiple applications.