Limit advertiser tracking. If you're going to restrict your children's access, you might as well restrict what marketers can do too, right? Under General, tap on About, and then tap on Advertising way down at the bottom. On the screen that appears, you'll find two options. The first one, Limit Ad Tracking, provides an indicator to Internet advertisers that you don't want them to track which ads you've viewed and engaged with, so they can show you ads that they think may be better suited to you.
The second option on this screen is a button to reset your advertising identifier--a new creation of Apple's in iOS 6; it's meant to be an anonymized tracker that advertisers can use to recognize your interest when showing their ads in apps. Apple doesn't yet require that in-app ads use the identifier, but says that one day it will. If you start seeing in-app ads that seem to know you too well, you can reset your advertising identifier here to start from scratch.
Manage storage on your device. Maybe your iPhone won't let you snap another photo. Perhaps your iPad refuses to let you download one more app. Because iOS storage space isn't expandable, it's important to monitor what's gobbling up the available gigabytes on your device. Here's how. Go to General > Usage in Settings, and wait for a moment or three as iOS calculates which apps are using the most space.
Often, Music and Photos & Camera are the two biggest offenders. If you use a service like iTunes Match, you can safely delete the Music cache on your device to free up space. If you sync your device with your Mac to back up photos and videos, you can delete those photos and videos, too.
Elsewhere on the list, you'll spot the apps you use, sorted with the most storage-intensive ones at the top. If you see apps that you rarely use but that take up a ton of space, tap on them in the list, and then tap Delete App to remove them in an instant.
Manually manage iCloud backup space. While we're saving space, don't forget that you can control what iCloud stores for you in your online backup--especially if you're just using the free 5GB allotment that Apple offers. Find instructions here.