Simple thing...your ID. Make sure you have it with you (along with your fishing license) in case you are checked by the local game warden.
It seems obvious, but some people don't carry it with them when they are on the ice. It is a bad idea for this reason:
If you get checked by the game warden and your ID is
somewhere else, you will waste valuable fishing time
trying to convince the game warden you are who you say
you are. Don't waste that time. Have your ID handy.
Next up: A compass