In my experience, the DMV (or whatever its called) likes to see you in person for license renewals every so often. Get a new photo, make sure you can see the eye chart.

I've always gone into the DMV when I purchased a vehicle from a private party. In California, it has taken me a couple visits; the first visit with the title and sale documentation, the second with the emissions test documentation that the seller was legally suppossed to provide at the time of the sale but practically, the buyer must provide to register the vehicle. Maybe you can do this by mail, but if you do it in person, you walk out with documents so you can legally drive the car. If you buy a car from a dealer, they take care of this paperwork for you, which used to mean having someone stand in line at the DMV and process a bunch of transactions, but now they can typically do it electronically.

If you move to another state, you need to get a new license and retitle and reregister your car; this usually happens in person, and most states have a requirement to do it in under a month. If your car has a loan, expect multiple trips to get it registered... the first trip will let you know what you need from the finance company; the second will bring that back and get registration; then when you eventually pay off the loan and get the title, you'll need to bring that in so you can get the title issued in your current state.