I am of the opinion that in the United States you need very little in the way of repair parts or tools with you on a tour. Obviously, you should do a major overhaul on your bike before leaving on any long trip. You should have all bearings inspected and repacked, all cables replaced, new brake pads, new chain, etc. quality bike parts last a long time so your chances of having a problem in the first place is reduced significantly if you put some effort into preparations.
On the ride, you certainly should be prepared to handle multiple tube punctures (spare tubes and patches) and a tire failure (tire boots and possibly a spare tire). A kevlar "Fiber Fix" emergency replacement spoke is a good idea in the event that you have a spoke fail. One or two of these should suffice and it beats trying to carry at least one of each size spoke (probably three different spokes) and a tool to remove the cassette to replace the drive side spoke (which is the one that fails most often). One spare brake and shifter cable might be worth taking if it's a long trip, but if you start with new ones, it's unlikely you will need them.
You should carry a multitool that has a spoke wrench and chaintool as well as wrenches for all the fasteners on the bike.
The above should let you handle 99% of problems you are likely to encounter. Major failures such as broken hubs, Bottom Brackets, and such, usually require special tools and parts that you are unlikely to have. These parts are generally not repairable in a campground, so there's no sense worrying about them. Just be sure that everything is good before you leave.
In the event you do have a failure that you are not prepared to fix, either find a bike shop (probably not one nearby!) or any telephone. Keep phone numbers for Performance, Nashbar, your favorite LBS, etc. handy and order whatever you need. FedEx delivers virtually everywhere in the US overnight. so you can get parts and tools quickly. If you have the tools at home, or leave them with a friend, you only need to pay the shipping cost to get them to you.
Outside the US, you may need to be prepared to handle more serious repairs. However, read some of Anne Mustoe's books on her cycling trips around the world. She claims to know nothing about how to repair her bike and does not even fix a flat. And she's ridden around the globe at least three times!