What wrenching skills/tools do I need for independent touring?

[Eden]

hmmmmm from the experiences of things that can go wrong on a tour.

Change a flat - of course #1

Adjust brakes - no one has fun riding with a rubbing brake

Adjust derailleurs - know how to use both the barrel adjusters and the limit screws

basic wheel truing - doesn't have to be perfect - just know enough about a spoke wrench to get yourself to a populated area/bike shop. Think about carrying a temporary kevlar spoke and know how to use it, if you'll be in very remote areas or gone for a significant amount of time.

spare cleats - cleat bolts. Really ruins the fun when you can't connect to your pedals...

chain maintenance - I've never snapped a chain, but I know some who have.... again for remote areas or long tours, I'd carry a chain breaker (the Park Tool Pro one rocks!!) and a spare link. For really, really long/remote tours perhaps a spare chain.

derailleur hanger? Again - probably only necessary for long tours or very remote areas, but I have know people who've bent a derailleur hanger just by having the bike fall over (and with panniers there's more weight if the bike falls on the wrong side)

know how to tighten your headset. This only requires allen wrenches, which any multi-tool should have, but there is technique involved. I've learned this one pretty well as mine seems to loosen a bit more often than I like... though I don't want to over tighten, as I have a carbon steerer...

Those are the things that I can think of. Some of them I'd only worry about for tours of longer than a few days or in areas where you'd really couldn't get any help in the case of major problems. Haines (yeah the automobile manual folks) actually makes a quite good bicycle maintenance manual. I've used to quite a bit. Park tool has good online tutorials.