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.

Untethered jailbreak
for iOS 7.0-7.0.5

As of February 18, 2014

If your device is not jailbroken on iOS 7.0, 7.0.1, 7.0.2, 7.0.3, 7.0.4, or 7.0.5: You can use evasi0n7 to jailbreak it untethered.

If you want to upgrade your device from an earlier iOS version:

You may choose to restore your device with iTunes in order to upgrade your device to iOS 7, and then jailbreak it with evasi0n7 to get an untethered jailbreak. Note that Over The Air (device-based) upgrades do not work on jailbroken devices.

Make sure to do an iTunes or iCloud backup of your data before restoring, and write down your Cydia packages so that you know what to reinstall after restoring and jailbreaking again.

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".)