Your average microphone stand is likely to come with one of two screw threaded mounting points. 3/8 inch screw threads are the standard in Europe, and the mounting point of almost every American-made microphone stand will have a 5/8 inch screw thread. If your microphone clip, shockmount or other stand-mountable gear doesn't fit, then it can be a good idea to kit yourself out with a screw thread adapter.
5/8" to 3/8" Adapters: They Usually Come Included
If you've finally picked up that new microphone but the included microphone clip is too small to fit your microphone stand, then stop yourself from reaching for a roll of gaffer tape and take a closer look at the base of the microphone clip. Usually, the inner 3/8 inch thread can be unscrewed using a coin so you can remove it to reveal a wider 5/8 inch mounting point, which will fit your stand.
3/8" to 5/8" Adapters
Sometimes, you'll come across a microphone clip with a fixed 3/8 inch screw thread that can't be removed. This is usually the case with older European microphones, like older generations of the Sennheiser MD 421. So, if you want to mount your microphone on a 5/8 inch stand, then you'll need a 3/8 inch to 5/8 inch screw thread adapter.
Mounting a Microphone on a Camera Tripod (3/8" or 5/8" - 1/4")
If you're working on a film set, then there'll be a lot of tripods with 1/4 inch screw-threaded mounting points around. So, if you need to mount a microphone on a camera tripod, you'll need a 3/8 inch to 1/4 inch screw thread adapter.
Mounting a Camera on a Microphone Stand (1/4"- 3/8" or 5/8")
Large DSLR cameras and professional film cameras are usually too heavy for normal microphone stands, but something like a GoPro can easily be mounted on a microphone stand. You could even stick one on a boom-arm microphone stand so you can suspend it over the drum kit. All you'll need is a 1/8 inch to 3/8 inch screw thread adapter. And just in case, handheld recorders almost always have a 1/4 inch screw-threaded mounting point.