The main advantages of jailbreaking:
1. Forbidden iTunes Store apps - you can add Apps that the Apple store prohibits.
a. PDANet - a program to tether your iPhone to a laptop via WiFi or USB so that you can surf the internet using the cell phone data connection on the iPhone.
b. Backgrounder & Insomnia - programs to run programs in the background. For example, an IM program so that even when your phone is sleeping, or you are using another app, you can still get IM messages.
c. SBSettings - this isn't a really compelling app, but I love it. It allows easy access to key functions - like turning WiFi and Bluetooth on and off - from the main GUI screen.
d. Swirly MMS - a full featured MMS app that allows you to send and receive MMS's
e. Winterboard - a replacement for the main GUI interface that allows complete manipulation of icons, backgrounds, sounds, etc. You can add scripts to backgrounds and the slider screen (like a script to display an analog clock instead of a static photo).
2. SSH and file transfer - you get access to the file system of the iPhone and get command-line Unix access to the phone by SSH'ing into it. So you can drag and drop files, pull up a process list on the phone, and it basically makes the phone feel more like a mini-laptop. Whether or not you think this is cool, depends on your perspective I guess. But the idea that I can SSH into my phone is pretty cool.
The main disadvantages:
1. Updates will erase it and you'll need to do it over and over.
2. You need to wait until after a firmware release has been out a while before you can jailbreak it - the hackers need to figure out how to crack the new release. Sometimes there's no wait, but often there's been a multi-week delay.
3. It's easier than it used to be, but it's still not something I would recommend to my mother. It requires a level of tech knowledge to be comfortable doing. At various times, I've gotten errors with it that required re-flashing.
4. You have to deal with the hacking scene. This can be cool - I personally like it - but which tool you should use depends on who figured out things first. The present solution of Pwntool'ing was preceeded by ZiPhone which was preceeded by iBrickr. There's also a certain level of the fact that you have to trust a group that you don't know much about to do "the right thing" with your precious iPhone and not turn it into a spam zombie or something.
5. Some of the hacked apps introduce instability - not as much a problem nowadays, but I remember a few crashing bugs in Summerboard (Winterboard's predecessor).
6. Some of the hacked apps use more power than typical (Paranoia, and OpenSSH used to).
7. Some of the hacked apps introduce safety concerns - with WiFi on, and OpenSSH running, in theory anyone can log into your iPhone and do anythign they want to with it.
My iPhone is jailbroken and I run Backgrounder and SBsettings and I love it.