The stem comes in two main flavors, the quill or threaded stem and the thread. Both work great.
Quill stems are most common on older road bicycles and usually come in the 1" variety. This means you would need a 1 inch threaded for to use a 1 inch quill stem. These usually have a clamp diameter of 25.4mm or 26.0mm depending on the manufacturer and when it was made.
Threadless stems are found on most modern road and mountain bicycles. For modern road bicycles the most common size is 1 1/8" stem diameter to accommodate 1 1/8 inch forks and 31.8mm or 26.0mm handlebar clamp. The 31.8mm handlebar clamp accommodates oversized handlebars. The idea with oversized handle bars is that having a larger diameter will increase the strength/stiffness of the handlebar.
Modern mountain bikes (mtb) use a 1 1/8 inch stem and 25.4mm or 31.8mm bar clamp.
If you have an older road frame and 1" fork that you want to convert to threadless from quill it is possible. You can do this either by finding a 1" threadless stem or getting a shim that converts a 1 1/8" to 1". These can be found at your local bike shop (lbs).