How many different career fields are there in the US Army?

The Army has 24 CMFs (Career Management Fields) aka "branches"

http://www.goarmy.com/rotc/careers.html

The combat arms (11, 12, 13, 14, 15, 19, and 18) will have the most command opportunities as will certain combat support CMFs (25, 31, 91, 92 and 88)

The least opportunity will come in 42, 74, 35, 56, 38, 63, 27, 62, 67, 65, 66, and 64

Which is why you see a lot of AG (42), 74 (CBRN) and 35 (MI) Officers in command of basic training units. For them any command is a good command.

For a combat arms officer a basic training command is the kiss of death (unless it is a second command - even then it isn't highly prized)

Edit:

Infantry, Field Artillery and Armor are where most Generals come from...mostly from Infantry and Field Artillery...those are the branches with the largest number of people and largest organizations

http://www.goarmy.com/careers-and-jobs.html