The most common are the Alnico rod and bar types used in most instrument pickups. Some common grades are:

Alnico 2 10Al, 19 Ni, 13 Co, 3 Cu, Bal. Fe
Alnico 3 12 Al, 25 Ni, 3 Cu, Bal. Fe
Alnico 4 12 Al, 27 Ni, 5 Co, Bal. Fe
Alnico 5 8 Ni, 14 Ni, 24 Co, 3 Cu, Bal. Fe (most common)
Alnico 8 7 Al, 15 Ni, 35 Co, 4 Cu, 5 Ti, Bal. Fe
Ceramic 7 MO-6Fe2O3
Cunife 1 60 Cu, 20 Ni, 20 Fe
There are various dimensions and grades used for specific purposes and even variations or tolerances within each. Ceramic magnets are also commonly used in pickups and are much cheaper than sand cast or sintered Alnico magnets. Fender has used various sizes of rod magnets and different lengths to compensate for the different output of each string. Due to modern alloys and better consistency, the strings being manufactured today have a pretty good balance or output from string to string and pole to pole.