I'm not an owner, so bear with me. Several responses included socket tools, safety wire, and safety wire pliers. Why?
By it's nature, don't safety-wired nuts stay on? (Yes, I still check them on my preflights on my rentals.).
Would the need for these things be if you noticed on a preflight that your mechanic failed to safety wire something, or forgot to torque an engine bolt or a bolt holding a magneto, for example, and you need to make a field fix before getting it to your (or any) mechanic?
On our airplane, and oil change requires safety wire. The oil filter is safety wired such that it can't spin itself off of the adapter. That'd be one example.
Some of the allowed pilot maintenance items may also require it as you learn to do your own MX items also. Depends on your airframe.
There's also the quintessential "I'm stuck at an airport with nobody and going to freeze to death because I forgot to pack something warm to wear..." (Hmm: A new set of items, your survival gear that stays in the aircraft full time, if you're into that sort of thing... And/or the model that you'll only have with you what you have ON you, and a survival vest... Survival gear is a completely different topic)... And many are mechanically inclined enough that they'd toss the new alternator belt on the airplane without thinking much about it (legalities aside) and fly home, to a nice warm bed.
Some owners carry all sorts of common failure spare parts, for that scenario, or even just to hand to the local A&P so they don't have to wait two days to have the part shipped to them to stick on your airplane. Just a box of stuff that's always in the back and always in the W&B calculations. Often that box includes the correct hand tools to do those things.
Personally I don't carry many spares in the airplane. I carry more spares in my truck (fan belt, etc) than the aircraft. But if I spent more time in lightly inhabited territory, I would reassess that decision. I do carry a small toolbox with simple hand tools. Not being able to launch because some stupid screw worked loose behind the panel or something generally innocuous like that, which may or may not be legal for me to touch, would be dumb.
Example... And a legal one... We once took some damage to a wheel pant (I'd just remove them if I could altogether but the co-owners like the look) and I spent a half hour removing the damned thing on a ramp paved with asphalt in the hot sun, so we could fly the airplane home. The hand tools in the toolbox made that possible. Get the thing off so it won't drag on or damage the tire, and deal with it later.
No tools, you're standing there wondering if someone will loan you some or if they'll charge you $75/hr+ and/or a weekend call out charge, just to remove ten or so screws and pop the fiberglass fairing off.
That said, I've met a few pilots who weren't blessed with the "mechanical" gene who shouldn't be allowed within ten yards of a screwdriver. If you're that guy, all you need is a charged cell phone and a credit card. Seriously. If you're not up to something, just leave it alone and have someone show you how.
I won't do tires. They're allowed for pilots but split rims and inattentiveness can kill or maim and I also just have no desire at all to be jacking the airplane up. I'll happily pay the money.
One thing I hate about the new GATS jars and what not over the old school fuel tester is the loss of a decent Phillips screwdriver on the bottom. That screwdriver works great for popping the cowl off of our 182. Fits perfectly.
