What tools should every guitarist have to do most small/medium projects for their guitars? (change strings, tuners, knobs, pickups)
A good multi-tool, like one by Leatherman, is a nice addition to your case. They include slot and phillips head screwdrivers, pliers, diagonal cutters (good for emergency wire stripping), a file (useful for fingernails).
In addition, I throw in a small set of real diagonal cutters for changing strings, because they work more easily than the one on the multi-tool. It's surprising how strong strings can be and these will make short work of cutting the string after you've detuned it until its slack.
Finally, I keep a small socket driver sized to fit 1/4" jacks on effects and guitars and amps, because, sure as shooting, they'll loosen.
A small bar towel is good for wiping off sweat and grime; Sometimes we get rushed during set up and don't get a good chance to cool off, so you can drape that over the upper bout of the guitar to keep a sweaty forearm off the finish. Sweat soaks in fast and takes a lot of work to get out so its better to avoid it. Towels also come in handy when you drop an amp on your finger, spill water, soda, beer, etc. Just toss it in the laundry and throw a clean one back in the case.
In addition, one or two small micro-cloths can help for touchups, especially if they have a bit of carnuba wax (or whatever sort of wax you use.)
My final thing is personal choice - I keep all my picks in an Altoids tin. In the old days it would'a been a Sucrets throat-lozenge box.
On top of everything else, it is always useful to have a kit of Allen keys, like these ones are very useful. The smaller ones are used for adjusting action and intonation on some types of guitar bridges, the larger ones, are for adjusting truss rods, if you do that sort of thing yourself.
To add to @the Tin Man's already awesome answer, you can try this little guy out for all the nuts/sockets on your guitar. I don't have personal experience with it, but the concept seems sound.
I usually keep one of these in my guitar case. It's great for doing on the spot setups for other players, and double checking to make sure my own instrument is kosher.
You could also keep one of those little string windy combination peg puller thingees (yes, that's a technical term), but in my experience they are very cheaply made and usually end up breaking after a couple of hundred string changes.
Here is what I have in my kit (although I am sure my kit is probably a little overkill) and to be honest I don't use all of these tools, they're just there in-case I need them.
- Battery powered string winder. (kind of looks like a cordless drill) handy for getting your guitar stringed up fast.
- ToneGear String Cleaner or GHS Fast Fret. Handy for cleaning your strings after use, although I always forget to use this, hence why my strings rust badly.
- Big Bends Nut Sauce Tuning Lubricant. This stuff is awesome, seriously. Handy if you know what it's like to buy new strings, only to have them break while you're restringing your guitar (it happens).
- A screwdriver set that has both phillips and flat head tips in it. A good variety of small and large screwdrivers is a good idea, especially for those tiny screws you sometimes encounter on pick guards.
- A multi-tool. As mentioned by everyone here, the bike riding ones are generally the best. Try and stay away from the cheapy ones, don't be lured and fooled by the cheap prices, once you've cut a couple of strings, the wire cutting snips on the tool will go blunt and sometimes break.
- A small allen key set. Even though a multi-tool sometimes has allen keys, you'll find that you might need a size that your multi-tool doesn't have.
- A nice cotton cloth. You can use it to wipe down the body of the guitar. I use a little bit of lemon juice when cleaning my guitar and it works so damn well. You can use it for your fretboard as well.
Multi-tools made for bike riders can be very handy. They're compact and have screwdrivers, and allen keys built in. Other than that I tend to carry a pair of needle nose pliers with wire cutters built in.
In addition to the Roadie Rench, I have a microfiber cloth (for wiping off the guitar), a CLEAN cotton diaper (for wiping my face and hands), a bar towel (for spills etc.), a spare guitar cable, a spare speaker cable, a spare set of new strings (and the last set pulled off), a dull sharpie pen (for my friends use), a sharp sharpie pen (for me!), a cheap back up guitar strap, a small bottle of Lysol spray & Fabreeze (to disinfect and freshen bad breath mics) (business cards, replacement fuses, a spare phone charger, a regular Bic pen, a spiral bound notepad and a ground adapter plug (to eliminate 60 cycle ground hum).