Hoo-boy, where to start!
It is simply amazing how many things can go wrong with a bicycle. I probably ought to make a list of the repairs I make, for future inventory procurement. But it also varies kind'a randomly -- last year I suddenly needed a large number of crank bearings. But I will list what comes to mind now.
Inner tubes.
Tires.
Pedals.
Crank bearings, primarily for one-piece cranks.
For three-piece cranks, the little bolts/nuts (depending on bicycle) that hold the crank arms on.
Aluminum crank arms also, because the pedal-threads get stripped out. And on the right-hand side, the sprockets get bent.
Sprockets get bent on one-piece cranks also, but those sprockets can be replaced, so you need only bring sprockets.
Chains don't need replacement as often as one might think, but of course you want to have some -- both 1/8 (single speed / hub gears) and 3/32 (derailer gears).
Rear wheels.
WD-40.
Most tight bearings can be fixed by simply loosening them a little, to make room for the inevitable dust. But in the absence of tools or time, a squirt of WD-40 will often wash them out for a while. Water works fine for this, but triggers instant corrosion.
Freewheels that either lock up tight or spin freely (more common) can usually be fixed by patiently trickling WD-40 into them. Make sure to identify the narrow gap between the rotating part and the stationary part -- that's where the WD-40 can get in.
Saddles.
Hand grips or masking tape. A bare handlebar can get too hot to touch.
Cables -- a couple of six-dollar cable tune-up kits. The Schwinn brand (K-Mart, I think) has nylon liner -- recommended. The Bell brand (Walmart) does not have liner.
The little metal loop that secures a coaster brake torque arm to the left chain stay of the frame, with screw and nut. Must. Be. There. And connected.
Now a couple of points about derailer. Derailers, with cable and shifter-device, are almost as troublesome as brakes, and that's saying something. On bicycles with two derailers (front and rear -- bicycles with 10 or more gears) I perform a preventive front-derailerectomy on most my bikes. Put the chain on the middle sprocket and you are golden.
But the rear derailer cannot be removed, because it tensions the chain, and derailer bikes have no other chain adjustment. Some folks advocate removing the derailer anyway, and shortening the chain to match -- and some of those bikes get carried into my "shop" with the chain as tight as a guitar string, utterly unrideable. (The chain "walks" up to a larger cog.)
To fix a useless derailer, it must be jammed fast in a position that provides a usable gear. You may be able to do this by simply turning in one of the tiny adjustment screws. But the screw may not have enough range, in which case you use bailing wire or some such, and tie the derailer in position. You will need pliers to twist the wire tightly until you have it just right. You will probably also take a while to figure out where to put the wire. This is major Micky-Mousing!
I hope that helps.
