I started doing some short tours a couple of years ago. Since I was in college at the time and didn't have much of a budget, I found an old (probably 1993) Rockhopper frame with a rigid fork, got a variety of components from E-bay and my local bike shop, and put it all together into a pretty nice setup for about $700.

Some comments from that experience, and from a friend of mine who tried doing the same thing with a newer MTB:

First, old mountain bikes work better for touring. All new MTBs have suspension forks, so you can't carry front panniers. This isn't a serious problem unless you are carrying a lot of weight, but putting all your gear on the back can mess with the handling. Also, older bikes, because they don't have suspension, have more relaxed frame geometry, which is usually more comfortable if you are spending all day in the saddle. It also lengthens the chainstays so you get more clearance between your heels and the panniers.

Second, don't skimp on wheels. 26" wheels tend to be quite sturdy, but think about hitting a pothole with 40lb of unsprung load on the rear wheel. I suggest some kind of freeride wheel, if you can still find one with braking surfaces.

Third, use cantilever brakes. V-Brakes and Disc brakes, while more powerful, can interfere with your cargo racks. If you can find racks that get around this, more power to you, but the weird outrigger things that disc-compatible racks use place very large stresses on the mounting bolts, and fatigue them quickly. Needless to say, it is really bad to be in the middle of nowhere and have the rack break off the back of your bike. The other concern I have about disc brakes (which may not be as serious) is the kinds of stresses that the front brake would place on the fork when trying to stop a loaded touring bike. In addition, if you use road-style brake levers (see below), these will work fine with cantis but not with V-Brakes.

Fourth, either get drop bars, dirt drops, or bar ends. You should have several different hand positions to avoid killing the nerves in your hands.

Minor notes: you should go ahead and use the entire mountain bike drivetrain (possibly excepting the shift/brake levers). I tried using a road triple crankset, and it works OK, but there is really no good reason to have a 53-tooth chainring on a touring bike, and sometimes its really nice to have the 22- or 24-tooth small cog.