I just changed the battery in my car and put the battery cables on backwards now the battery won't charge I tried a different battery and still wont work. Could I have damaged the alternator?

when you reverse connect a battery there is a good chance you will blow the main fuse this will protect the car from more damage but usually stops the battery for been charged as well... check and change the main fuse or fuseable link The alternator probably already was bad before you put the battery in.