Back when I had older iPhones, I jailbroke them (circumvented Apple's software approval process) to get all the features it didn't currently support: a dimmer, warmer screen at night, file management, wifi tethering, and one-tap controls for certain features.
With iOS 8, Apple has taken care of most of this natively, so I don't have a huge need for jailbreaking. However, there are a few non-Apple-sanctioned features I really like.
F.lux lowers the color temperature on your screen at night, to reduce eyestrain. I run it on my mac and love it. I would jailbreak just for this tool.
BioLockdown lets you enable password protection on any app– great when you want to hand your phone to somebody but don't want to give them access to, say, secret work files, or selfies you took in a tutu.
Zeppelin lets you customize or remove your carrier from the menubar: bye-bye, "AT&T" staring at me every day. Alkaline lets you tweak the display of the battery indicator.
Historically, I've found that some jailbreak apps, particularly Winterboard, seem to slow the device down. This time around, I don't see any of that, though I've also skipped over Winterboard because the stock iOS8 theme looks great to me.
Jailbreaking lets me round out a few of the rough edges Apple left in their latest OS, and tweak this hunk of metal and glass to fit me even better than it did before. If you have a decently new iOS 8 device, give it a go.