Apex is one of the most popular and established launchers. It comes with almost every customization that you could imagine: infinite scrolling, fancy transitions, custom styles, gesture controls, drawer sorting, immersive mode, and even more with the Pro version. You can hide unwanted apps — such as carrier bloatware, lock your homescreen to prevent changes — useful if you hand your phone off to kids or tricksters frequently, and you can apply a vast array of themes. Apex Launcher requires at least Android 4.0, but that shouldn't be a problem for the majority of Android devices.
Apex Launcher is also good at both trying to keep their permissions down and explaining what each one is used for, a helpful piece of trasparency we wish more developers adopted. Apex is free, but the Pro version is $3.99, and worth it if you're someone who delves into a launcher to make their phone truly their own.