Jailbreaking. Everybody who’s had an iPhone for more than a few days and is remotely tech-savvy probably knows what it is: the process of modifying your iPhone’s software to allow code unauthorized by Apple to run on it. But why would you ever want to do such a thing? In no particular order:

1. Themes. The standard iPhone OS doesn’t include a way for you to change the background on your iPhone, or the lock screen, or to personalize your iPhone in any way. WinterBoard, which is a replacement for SummerBoard, itself named after the SpringBoard (the ‘home screen’). Themes let you change pretty much anything about the way your iPhone looks.
2. Tethering. Strictly speaking, this doesn’t involve jailbreaking, but given that it breaks in iPhone OS version 3.1, it’s assumed that Apple/AT&T doesn’t want you to do this. Simply open Safari, navigate to http://help.benm.at and select your carrier, then install the profile. Enable tethering under Settings -> General -> Network -> Internet Tethering, and you’re set.
3. SBSettings. SBSettings is one of those things that doesn’t seem useful until you need it, and then it’s a lifesaver. Available in Cydia, and with its own section for plugins, SBSettings lets you enable/disable Bluetooth, 3G, Wifi, location tracking, and essentially anything you can toggle from the standard Settings.app, without ever leaving your own app. You just activate it by swiping sideways on the status bar, and set the toggles.
4. Cycorder. If you’re without an iPhone 3GS, you can use Cycorder, available through Cydia, to record video. Even if you do have a 3GS, apparently Cycorder has better video quality, at the cost of larger video files.
5. Running apps in the background. Pretty self-explanatory; install Backgrounder from the Cydia app repository (make sure to install the one appropriate for your software version; don’t install the 2.x on a 3.0 or vice versa!). Note that if you’re on a 3GS and you hold home down to activate voice control, that will enable backgrounding on that app (since Backgrounder uses a shorter timer than Voice Control), so you’ll have to disable it again afterwards. Or you could always exit the app and then activate Voice Control.

So how do you jailbreak? Install redsn0w, from the iPhone Dev Team (who’re obviously not the actual guys who dev for the iPhone). You can find torrents of it here; they’re all heavily seeded, so you shouldn’t run into any issues with respect to speed. It’ll work on any iPhone that’s not running the 3.1 beta builds, including 3GSs.  If you’re running into issues, or something breaks, you can always put your iPhone into DFU mode. How do you do that? Simple.

1. Plug it into your computer with iTunes.
2. Turn it off. If it’s completely frozen, hold the power and home buttons down until it turns off.
3. Connect it to your computer.
4. Hold down the power and home buttons again.
5. When the Apple logo comes up, release the power button; keep holding the home button until iTunes recognizes it and asks you to recover it.

Be aware that this will delete everything you have on the phone; so I recommend you back up often, especially with a jailbroken iPhone.