As you work more and more satellites, you will find that there are different awards that you can apply for.
Here are the ones I have so far -
Satellite Communicators Club(1 Satellite Contact)
OSCAR Satellite Communications Achievement Award (20 States/Calling Areas) (all done on UO-14)
South African AMSAT Achievement Award (25 Low Earth Orbit Satellite Contacts)
AMSAT 51 on 51
AMSAT Robert W. Barbee Jr., W4AMI Satellite Operator Achievement Award (1000 Contacts)
I am currently working on -
ARRL VUCC
ARRL WAS with Satellite Endorsement
You can check out this page on the AMSAT site for more information on the awards you can get.
I have worked the following birds - UO-14 (RIP), AO-16, AO-27, FO-29, SO-50, AO-51,VO-52, ISS