If you upgrade iOS with iTunes, your device will be un-jailbroken and Cydia packages will be deleted. Before upgrading iOS, make sure a jailbreak is available for the new version.
As of September 23, 2014
No iOS 8.x jailbreak
There is no jailbreak available for iOS 8 on any device, so avoid upgrading if you want your jailbreak.
Note that if you click "Restore" in iTunes, Apple will update your device to the newest version (iOS 8 for devices newer than iPhone 4), which will remove your jailbreak.
You can follow jailbreakers such as @PanguTeam, @evad3rs, and @MuscleNerd for news.
If you want to upgrade to
non-jailbroken iOS 8:
First backup your data with iCloud or iTunes, and then click "Restore" in iTunes to update to iOS 8 and lose your jailbreak. ("Restore" is better than "Upgrade" — that will probably work too, but you will lose some disk space until the next time you restore.)
You cannot OTA (Over The Air) update a jailbroken device.
iOS 7.1.x untethered jailbreak
If your device is not jailbroken on iOS 7.1, 7.1.1, or 7.1.2: you can use Pangu to jailbreak it untethered.
Note that afc2add does not work on iOS 7.1.x; you can use Apple File Conduit "2" if you would like that functionality.
iOS 7.0.x untethered jailbreak
If your device is not jailbroken on iOS 7.0, 7.0.1, 7.0.2, 7.0.3, 7.0.4, 7.0.5, or 7.0.6: You can use evasi0n7 to jailbreak it untethered.
Make sure to install SSLPatch if your device is on iOS 7.0-7.0.5 or 6.0-6.1.5.
How do I find my current version?
Open the Settings app, tap General, tap About, and look at Version.
(Your device's version is also listed at the bottom of the Cydia "homepage".)