You're gonna be bothered by how cool I am.

In the General Election, you can vote for whoever you want, regardless of party affiliation.

In the primaries/caucuses, it's different by state. In my state, you can vote for whoever (but with our computerized system, you have to tell them which party's candidates you want to choose from). That's an "open primary." But some states have a "closed primary" for one or both parties (and just because the Dems have that in a certain state doesn't mean the Repubs will, and vice versa), which means you have to be registered with a party to vote for its candidates.

If you change your views over the years, though, and want to be able to vote in a closed primary for a party you're not a member of, you have to re-register with the party of your choosing.