Why Jailbreak Your iPhone 4?
There are lots of reasons you would jailbreak your iPhone 4. The most common reason is to use this awesome phone on networks other than At&t or Verizon (or whatever network provides your iPhone 4 if you aren't in the USA). Besides using your iPhone 4 with other networks (this is commonly referred to as "unlocking" with other phones), you might want to install apps, tweaks, or themes that Apple hasn't approved for one reason or another. Like an austere father, Apple has become notoriously picky about the kinds of things it allows on its "perfect" child, the iPhone. Thus, a "black market," full of any possible app or tweak has flourished. And jailbreaking allows you access to it.
1. Use other networks than the phone was manufactured for
Wherever you are in the world, Apple has negotiated contracts to make the iPhone 4 exclusive. It has done this to keep the price high, secure control over use, and maintain an air of exclusivity and superiority for iPhone 4 users. This is quite contrary to most other smart phones, which compete pretty openly against other smart phones and networks. Contrary to many people's beliefs, iPhone 4 is actually the third most used smart phone, behind number one Android, and number two Blackberry. Jailbreaking and unlocking allows iPhone 4 owners to choose their network, which they might do based on price or network coverage wherever they are.
2. Install non-Apple-approved apps
Behind using a different network, this is the most common reason people jailbreak their iPhone 4s. Some of the apps available include apps that compete with Apple's own (like Podcaster) to sick games (like Baby Shaker). Another very popular app is SlingPlayer which allows you to stream TV from your SlingBox.
3. Install tweaks, screensavers, ringtones, and wallpapers
Jailbreaking your iPhone 4 opens up a wealth of interesting tweaks to nearly every aspect of your iPhone 4. Some of the things you can change are the menu, icons, screen saver, wallpaper, and function of the buttons. One very popular tweak allows you to use your iPhone 4's internet connection to tether other computers onto the web.
These are the top reasons why someone might jailbreak their iPhone 4. In my opinion, jailbreaking your phone really opens up your iPhone 4 to tons of functionality with pretty minimal downside risk. If you have a different opinion, chime in with a comment!