For what reasons do most states require voters registration?
All US states and territories require voter registration, simply to prevent voter fraud.
I'm pretty sure they all do. And the reason is to a) know how many registered voters are living there and b) prevent voter fraud. When you're registered to vote, it means you've already proven that you are who you claim to be and live where you claim to live. That way, nobody can show up to vote claiming to be you and you can't run around to different jurisdictions and mess with their election results.
To show you are a resident that is allowed to vote. Felons can not, non citizens can't. Illegal aliens can't. The card shows you are authoirized.
To eliminate voter fraud.