Advantages ( Pros ):
1. Some apps that can be downloaded from the appstore are available like CyCorder and PDANet. These apps are very helpful.
2. Cydia and Icy are two unofficial app stores that allow you to buy different apps, themes and games absolutely free. This is only available to those who jailbreak their device. There will be many fantastic apps that the app store had rejected and they will work perfectly with your device.This gives you another choice and you can choose apps from the app store and from the third party app stores like Cydia.
3. Get various themes for your device that are not available anywhere on the app store! You can only get these themes from Cydia and other third party software. Apple already supplies you with a pretty good interface but to add the 'cool' into it you'll have to get your device jailbreaked. Then you can make your device interface into a snow leopard or a vending machine. You can add more customization to your device and make it to whatever you want to! You can through this also add an additional dock and get new sounds for your device making it more like how you want your device!
Disadvantages ( Cons ):
1. Your warranty will be dismissed. This is sad, but it's true, a jailbroken iPhone/iPod will lose it's warranty and apple will not support or entertain any hardware issues with your device if it is in warranty. This may seem harsh but you can easily get around it. If you use your iTunes to get a clean restore for your device, Apple will not be able to identify if the device is jailbroken or not!
2. Once after a jailbreak, if you update your devices software via iTunes, your jailbreak will be finished and all your apps that were received through a jailbreak will also be erased. But the Dev-Team usually updates it too in a couple of weeks, you won't get the new software on release date.
3. Another major thing is that your iPhone/iPod will become more unstable. Every software crashes in a while including iOS but after a jailbreak there is a more possibility of crashes. These crashes will not harm your device in any way and you can reset your device. Generally, your device will also slow down a little.
4. There is also a very slight chance that your device will brick or in other words, get ruined and it will be wasted. This possibility is very rare and only 1 in 10 000 users will experience it. The dev-team has made everything real safe and user friendly but there are always risks of your device to brick
At the end of the day you will be thinking of either jailbreaking or not. If you ask me, I will say one MUST jailbreak his device to have the complete and the best experience of his/her iPhone/iPod. There are some cons, but the in overall, jailbreaking will be better. The cons are not too much of a problem, and you will be getting all the cool advantages if you jailbreak. For the procedure of a jailbreak, go to http://applehelpp.blogspot.com/2012/06/jailbreaking-cydia-installous-iphone.html