iOS (jailbroken): It doesn't take all that many taps to go in and update your apps on your iPhone or iPad, but if you would prefer it just happened automatically in the background, Auto App Updater is a jailbreak app that does just that. With Auto App Updater installed you can pop into the Settings on your iOS device, and configure it to automatically install app updates for you at timed intervals.
When it's set up, Auto App Updater runs in the background at set intervals to check for updates and installs whatever is new. When it's done, it sends you a notification saying how many updates were installed. You can blacklist apps from updating, and you can also dig into the update history to see what's new.
Unfortunately, you can't set up a specific time for Auto App Updater to run, but you can restrict it to Wi-Fi only so you don't use up any of your mobile data allowance. Auto-updating your apps isn't always a good idea, since an update occasionally breaks functionality, but this is useful if you're willing to risk it.