I prefer individual hex keys to a multi tool because they are easier to get in to tight spots. You can also leave the sizes that you don't need at home.

Steel tyre levers are narrower than the plastic ones and are easier to get under a tight bead than the wider plastic ones.

Finally a small spanner for those mud guard stay bolts 

I ALWAYS carry a spoke wrench. And of course a tire pump and patch kit which aren't necessarily in the "tool" category.

It's interesting, the different opinions of necessary. I don't even own a spoke wrench, much less carry one on a daily basis, and only vaguely have an idea of how to use one. 

Early in my cycling career I did have wheels that suffered broken spokes. I moved to 36 spoke wheels, and have been care free ever since. I did carry appropriate length replacement spokes for awhile. But it's been so long now without problems, I haven't asked for spokes the last couple of bikes I bought.

Perhaps I ride under a golden star. I'm no mechanic. I can change a flat and do the simplest of adjustments. My approach is to take my bike to a qualified mechanic before a tour. That method has served me well. 

Thus, I carry the typical flat changing tools, and allen wrenches. Flat head and Phillips screw drivers. Now I have a bike with couplers, I carry a wrench for that. I have had a small adjustable wrench, but think it might have disappeared. I did have a good quality, small pedal wrench that also disappeared. I blame Jacinto for taking my tools and not putting them back. He, of course, is innocent. 

Not exactly tools - but I carry a small pair of scissors. They've come in handy a number of times.

Kelly, I use a spoke wrench to keep the wheel true, and to keep the spokes tight if I find loose spokes. I true/tighten spokes regularly. My last broken spoke was 20 years ago.

I take way more than I need, but for me it's part of the being "totally self-sufficient" gratification that I get from touring... the fact that everything I need is with me. I suspect that's going to be changing in the near future as I get tired of carrying around things that I don't use, but for now....
I'll be interested in reading the responses of the couples who travel several months every year.

Tools:
patch kit
spare tube
emergency tire boot 
tire tools 
Crank Brothers speed lever
25-in-1 tool  
small needle nose pliers
small crescent wrench
pedal wrench 
saddle wrench
grease
oil  
Fiberfix
cleaning cloth
degreaser
degreasing hand cleaner
duct tape 
electrical tape
handiwipes
miscellaneous nuts and bolts  

My tool kit is so close to Mark Bigham's that we may as well say they are the same.   Obviously, great minds think alike and assemble similar tool kits.   Perhaps Mark and I should assemble some spare kits and start selling them as the "Great Minds Tool Kit."  Of course, having the tools is only half of the battle; you need to have the skill and mechanical aptitude to be able to effect roadside repairs with the tools.   And that's where I'm sometimes not so talented...

I carried a pedal wrench a long time ago but have no use for it now because it has been more than 20 years since I owned pedals with flats for a spanner. For decades, my pedals require a 6mm or 8mm hex wrench for installation.