Having a shed without power at one end of the garden and a nice warm kitchen with light and cups of tea (along with an understanding mrs trekker who agrees it's a good idea to tinker with her bike in the kitchen) means I often dive into the saddle bag for tools and spares rather than lugging my main bike box all the way down the garden. This means I pretty much know the travelling tool kit fixes any part on the bike I can think of.
I addition to a multi-tool, on tour we take an 8mm spanner, a 10mm spanner (because I was daft enough to buy two types of mudguards and they each have different sized securing bolts), the Leatherman is used in the camp kitchen as well as a bike tool, a spoke key, a half roll of electrical tape (although cutting it in half leaves lots of short strips rather than a roll
) and two 10 speed chain links. Oh and a bottle of chain lube.
For spares we take one gear cable and one brake cable and a pair of brake pads for each bike (one is disk, the other is caliper). On the basis that we shouldn't break a cable each on the same day and we can either get to a shop or take a day off and wait for the magic of the internet. Both bikes also have at least one spare spoke taped to the down tube of a length I'll get away with a temporary repair no matter of it's location.
Perhaps we travel a little light but on our only big tour so far (two weeks in well populated Europe) I hardly raided the tool kit except for basic maintenance. As it was a learning exercise I listed everything we carried and didn't use and don't intend to take again, so, next Summer along the Danube it looks like we are only taking a bottle of chain lube and one inner tube!!
ETA oh and cable ties, thanks Jurek, and I'm knicking that storage idea, mrs trekker hates finding them shoved in any pannier pocket I've found space so they poke you in the eye every time you open the pocket!