To expand a little on what Mike said....
Basically boils down to two categories: non-airbrush compressors and airbrush specific compressors.
What I mean by non-airbrush compressors are the ones you buy at hardware stores which are intended for use with air tools (nail guns, impact wrenches, etvc). Range in price from about $100-$1000+, although for our purpose the absolute low end of this is what you are looking at. Even the smallest ones are pretty substantial in size/weight, feature a tank of some sort, with gauge and regulator (at least I've never seen one without). They "just plain work" but they are just plain noisy to one degree or another. Modelers who are fans of this type like to point out that the noise is not persistant: usually they will pump the tank up to 100lb or so and then shut off, kicking on again only when the tank pressure drops far enough (some modelers even claim to get a whole coat of paint on a model without it kicking back on). They never come with moisture trap (at least at the low end), though the tank itself provides some of that functionality.
Airbrush specific compressors are, with little exception, rather quiet to near-silent and much smaller/lighter than the hardware models. Prices range from about $200-$2000. At the very low end they are not so much compressors as they are air pumps, without any control over pressure or anything (they run continuously and bleed excess pressure if you stop airbrushing). Next up are models with regulator and/or gauge, and or moisture trap, and because they dont bleed they usually have an auto on/off (they stop when you stop so as not to wear the motor out). These are where the fun begins. Then come models with reservoir tanks which eliminate the ever so slight "pulsing" of air which the tankless ones can exhibit, then come the totally silent ones, and so on.
IMO if one is on a budget and needs a compressor, the hardware store stuff is fine (light years ahead of using a spare tire <g>) but if dont need one right away and can save up a bit, spending about, say, $300 for a decent airbrush specific setup is worth the size, noise, and utility to me (I was lucky and got a rebuilt T&C from Badger for a cool $100).