I wish it were possible to peg John's response up near the top, as he's boiled down many posts into a single, well-written response with a good foundation.
However, fools rush in, so I'll add "things I look for in a touring bike" on to his answer. Note almost all the bikes currently sold for loaded touring meet almost all these additional requirements.
- Low gearing. I think it's almost impossible to get too low, but 20 gear inches is a good maximum minimum gear. 16-18 would be better. Honestly, you won't care too much about the high gear, but anything over 100 gear inches will see pitifully little use.
- Long chain stays. Keep big feet from knocking rear panniers.
- Provision for mounting front and rear racks. You can use P-clamps (except maybe on carbon), but it's really nice to have everything build into the bike.
- Good geometry for those front racks. I don't know what makes it good, but you'll have lots of fun wrestling with tight turns on a loaded bike; don't add to it unnecessarily.
- Provision for getting the bar close to level with the saddle. Some people like low bars, but most of us prefer to sit up a bit and see what we're riding past. Next to nobody complains they can't get bars low enough, but lots of people try to get the bars further up. Don't let anybody cut the steerer on a threadless headset until you've ridden it for a year!
- Built for wide tires. In 700C, that means 28 or wider. I prefer 32-35, and some people and makers like really fat tires, like 37-40. These carry the load at reasonable tire pressures, and absorb some of the shock that would otherwise end up at your tush.
- Room for fenders. You'll get some argument here from people who only ride in dry areas, but I dislike getting road spray on my shoes and chain.
- Room for at least two water bottles. Three might be better.
I'll add that for off-road and third-world touring, you might prefer 26" tires. You can make them work on the road as well, just by using slicks instead of knobby tires. In addition, though this may be more controversial, 9-speed seems to be the newest that's widely available.
Back to echoing what John wrote, do try out as many touring bikes as you can. Try to get them as close to identical fits as possible, but there's usually one or two that just ride better than anything else. Get that one -- you'll like riding it, so you'll ride it more. There's nothing sadder than a high-end bike rusting in the garage because the owner doesn't like to ride it.