There are numerous reasons to jailbreak. Here is a couple of reasons I did.
1. Being able to change things with the operating system that Apple haven't made as standard (cydia tweaks)
eg: changing carrier to whatever you want,
Having a call recorder,
Stopping automatic/accidental updates of iOS,
Changing the font,
Adding different buttons to the quick menu for various options
2. Being able to download paid apps and games for free
Some rumours state it will be unsafe etc but I've jailbreaked since the 3GS and yes there have been some bugs but they normally get sorted quickly and as for security as long as you change the root password you're safe !
Any more questions please feel free to ask