Some of these, the Olloclip Essential Kit for instance, do have trouble attaching over phone cases, so you may need to remove it before you can start shooting, and all of them will leave vignetting in the corners of pictures if they aren't aligned properly. In terms of mounting options, most use clips that are fairly versatile in terms of the devices they can attach to, like the Xenvo Pro.
If you want a complete package with loads to play around with, the Shuttermoon Pro has 11 different options, so a great way to start getting familiar with what each lens can do. There is some variety in terms of which lenses are included, like the Black Eye G4 Kit substitutes the fisheye for its portrait lens, and others like the CamKix Universal Kit adds in a telephoto. It's becoming increasingly popular to package these add-ons in a bundle as opposed to selling each one individually, so kits like the Amir 3-in-1 HD and Olloclip Essential Kit with their macro, wide, and fisheye lenses are now the norm rather than the exception.
You may notice that most of the options here are kits rather than single lenses. Keep in mind that not all of these will work for every phone, so be sure to verify that you are looking at one that fits your needs before finalizing the purchase. That said, the Ztylus Revolver M Series and the Black Eye G4 Kit rose above the others and earned a spot among our top ten.
While there are a number of new items on the market competing with what was already on this list, most of them are somewhat low quality, with complaints of durability, image quality, and difficulties fitting the lens onto the camera.