If you want stability...
Nova was the launcher you all recommended most often, and with a good reason: It's steady, fast as hell, and easy to use. Upgrading to Nova Prime for $4 unlocks a few bonus features, including an immensely useful scrollable dock. It's available for Android 4.0 and up.
If you want something fresh...
Of all the launchers we tried out after our round-up last week, Everything.me felt the most like something new. The free launcher is currently in beta for phones running 4.0 and up. We're particularly fond of the homescreen search widget that queries your apps, messages, files, as well as the web for keywords.
Recommended by ChevyC10
If you want your home screen to look like stock Android...
Like Nova, Apex Launcher retains much of the core Android functionality but adds a lot of handy features—like widget resizing—as well as some super-deep customization like giving you the ability to set the duration of your phone vibrations. A $4 upgrade to Apex Launcher Pro unlocks loads of new features, including two-finger gestures. Like many current top launchers, it's available for phones running 4.0 or higher.
Recommended by PixelSnader
If you want your home screen to look like iOS
For a screen that looks like iOS in the Forestall era, check out the free Esper Launcher. Compatibility varies from phone to phone so you'll have to check to Google Play link so see if it'll work for you.
Recommended by Marty_LK
If you want your home screen to look like Windows Phone...
If your phone is ancient (and you're cheap)...
Unlike some of its newer brethren, Go Launcher EX has been around forever, so it's reportedly compatible with phones running OS versions all the way back to Android 1.6. Another benefit of its long existence is a massive community of users, and over 10,000 downloadable themes. And it's FREE.
Recommended by Inspektor