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 July 1, 2014

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".)