Find your keys; square, flat, gib-head, round...

Keys, along with keyways and keyseats, offer dependable driving connections between shafts and hubs.
Sensibly, key size is related to shaft diameters, those combinations are typically based on power to be transmitted. A secure connection occurs when shaft and hub diameters fit to engineered tolerances. A close fit reduces shearing action across the key, through key seat and key way depths, and key seat length, to a degree.
Those fits and depths are easily referenced via Machinist's Handbook, many manufacturers, and scores of web pages.
So, to energize this thread, I've prepared an illustration of various keys, along with comments.
Attachment 23163

FWIW, there are two programs on my webpage which relate to keyway calculations - KEYWAY and OFFKEY.

The former implements some typical square keyseat calculations. The latter, requested by a user, assists in the design of an offset key. I'm not familiar with offset keys but the idea is that if a small angular offset of the shaft position is needed after the keyways in shaft and bushing/pulley/etc. have been cut, a key that has the parts that enter the two slots angularly displaced is employed. An interesting bit of math goes into designing such a key.