Bikes are machines. And as beautifully simple and reliable as they are, even these machines are prone to wearing out. You need not be a master bike mechanic to enjoy adventure cycling. But it certainly will boost your confidence and decrease your worry if you know how to take your own bike apart and put it back together.
It shouldn't be too difficult for you to find a bike maintenance and repair class or to find loads of instruction on the internet.
The longer the distance of trip you plan to take, the more you should plan to bring in the way of tools and spare parts. For short day trips, you're probably fine just to bring an inner-tube repair kit, a spare tube, and a small air pump to fix flat tires. For longer trips -- several days and more -- experts recommend bringing spare sets of brake blocks, spare brake cable, a chain breaker, extra spokes, allen wrenches in all the sizes found on the bike, a small tube of lube, and a small toolkit capable of servicing common repairs on the bike [source: Barnes/The Adventure Cycling Guide].
If something really major goes wrong -- the frame snaps or a rim breaks -- your best option is to find a bike repair shop (or a welder) on the road. Fortunately, these services are fairly common in decent-sized cities and towns around the world.
And on that note, consider carefully whether you really want the feather-light titanium frame, innovative Rohloff Speedhub gears, and stop-on-a-dime disk brakes for an adventure cycling trip. They do make your bike special, but if they fail on the road, they could be difficult to service. And the more remote and exotic your trip, the harder it will be to find non-standard parts and people who know how to install them. Just something to think about.