Bullet speed, or velocity, is usually not measured in miles per hour (mph) but in feet per second (fps). You can however, if you desire, use simple math to calculate a given cartridge's mph using the following formula:
(Bx3600) / 5280
where B is the bullet speed measured in fps. (there are 3600 seconds in an hour, and 5280 feet in a mile)
That said, bullets of different calibers travel very different speeds. On top of that, different bullets of the SAME caliber can travel different speeds because of different weights, powder charge, pressure, etc.
The slowest and fastest bullets I can think of off the top of my head are as follows.
Many .45 Caliber hand gun rounds travel at apprx 870fps. This can very based on bullet material and weight, but 870fps is a good average. This equates to 661 mph using the formula above. (100 mph slower than the speed of sound)
Some custom loaded .243 rifle rounds (a small bullet used mostly for small game) can go a little bit more than 4000fps and have been recorded as fast as 5278 fps.
If you use 4600 fps as an average for the very fastest .243 rounds, you get 3136 miles per hour. (just over four times faster than the speed of sound)
Pretty damn fast.
Hope that answers your question.