My wife's bike recently got scraped up and the paint got scratched down to the frame. It's an alloy frame. Should she be concerned about rust or any kind of damage? If so, do we need to get it repainted? There are about three scratches, each about half the size of a dime.
Chromoly can rust. Aluminum usually doesn't unless you're riding in the ocean. Cheapest fix is probably some automotive touch-up paint; sand / clean the area (scuff the surrounding paint up a little), apply a coat, wet sand, repeat. Won't be perfect but it'll protect the underlying metal from rusting.
Of course, if you want that perfect "unblemished" look you're probably going to have to plump for a professional (read: take your bike completely apart, sandblast frame, re-paint, put all components back on). Unless you're looking for an excuse to get a completely amazing custom paint job. At which point I'd recommend finding a good powder coat shop; my mountain bike's (chromoly frame) is powder coated and has held up really, really well over the years.
I have had good luck with hobby paints. Most are enamel so they are durable. The cost is generally under $2 USD for a ½ ounce bottle.
You custom match your color by mixing paint in small amounts. My buddy has a Diamondback. His color is three drops of blue with one drop of black. You can experiment to find the right combinations. Always allow the test sample to dry as the color may change. This can be sped up by using a hair dryer on low setting.
Lightly sand the damaged area with very fine sandpaper, and wipe it with a solvent (rubbing alcohol works fine). Apply the paint with an artist brush. If the area was the result of cables rubbing, cover it with a patch of clear chainstay-protecting tape.
I have a powder-coated Brompton, that recently had small areas (~2mm) of the finish rubbed down to the steel by cable housings. To deal with this (the area was spotless, the cables had the steel polished bright), I just applied touch-up paint, and let it dry for days. I will smooth it with 1000-grit sandpaper, then apply helicopter tape once this is done.
As others have noted, if the frame is aluminum, it's primarily an aesthetic choice. But for steel-framed bikes, it's a necessity.