Technically, there is a JB for iOS 5 on all/most devices running iOS 5 (except the 4S, of course). It a tethered JB, though, meaning you have to plug the device into your computer every time you reboot the device. That and most of the software you'd want to use might not be updated for iOS 5 yet.
Previously, people would jailbreak for functionality like:
* copy/paste
* wireless iTunes sync
* using the volume-up button as a shutter for the camera
* wallpaper/theming
* install custom ring/text tones and notification sounds
* Spotlight-like search
* enhanced notifications (banners and on the lock screen)
* enable numerical battery percentage indicator
* blacklisting/blocking specific contacts
* quick-access utilities to switch services like WiFi and bluetooth on and off
* make the multitask bar rotate in landscape mode on non-iPad devices
* lock screen rotation in landscape mode
* ad-block for Safari
* download regular files with Safari, like on a regular computer
* access and use the filesystem directly, like on a regular computer
* access a command line shell and use UNIX utilities, like on a regular computer
* remotely display and access the iPhone screen on another computer
* add widgets to the lock screen or home screen, like Android
* use a finger-swipe pattern to unlock instead of a passcode, like Android
* unlock the iPhone for use on other carriers
...among many other things, that's just what I can think of off the top of my head.
A good portion of that list had now been made moot, as Apple has taken many of those ideas and implemented them into iOS proper through either outright copying (remember, Steve said he was shameless about stealing ideas and implementing them his way) or hiring the original developer (as in the case with the new notifications).
We still can't theme (look at what things like WinterBoard and DreamBoard can do), block numbers (iBlacklist), or quickly toggle services natively (SBSettings)....but maybe someday, or maybe never. Until then, there's the jailbreak for you. The sky's the limit when your phone is not longer restricted. With that freedom comes risks, of course, and generally you should be technically savvy in order effectively use and troubleshoot a jailbroken installation.
I personally intend to jailbreak in order to use SBSettings, which lets you quickly toggle services like WiFi and bluetooth on and off without having to dig through menus. Having been used to it since 3.x days, I'm finding it rather hard to live without.