I've had many moles removed over the years (lots of time spent in the Southern California sun as a child, and very fair Irish skin). Usually, they scrape them off with a razor, and in my experience, this does not leave a scar. You simply cover it with a band-aid, and apply Neosporin daily until it heals.
I've also had them removed via scalpel (not recommended, but probably not necessary unless they suspect skin cancer - this is the only method that has left a scar for me, because they had to cut away a large eye-shaped area and then stitch it back together... ugggggh). They also have a round hole-punch type thing that removes a round plug of skin - again, they wouldn't do this unless they felt the mole could be cancerous, and they're trying to leave a clear margin around the mole for testing purposes. The hole punch didn't leave a scar, either.
I've never had a mole removed via laser. I imagine it would be more expensive, and possibly not covered by insurance?