Recently I have been volunteering with a local youth organization leading Saturday rides. The kids in the program are riding bicycles that might be referred to as "vintage" or "refurbished." These are bikes, and bike components, that have seen some wear. The first ride that I went on, we saw one flat tire and two busted chains. We also have had cranks fall off.
Ideally, these are things to be avoided. A good habit to get into before you go for a bike ride is your ABC check: air, brakes, and chain.
Check your air: Mountain bike tire pressure can be around 30 to 50 psi, hybrids can be 50 to 80 psi, and road bikes can be 80 to 110 psi. Good floor pumps come with gauges. You should also come to know when your tires are properly inflated simply by squeezing them. On bicycle rides, I always carry tire irons, a patch kit, a portable pump, a spare tube, and tire boots (and have used them many times). I also carry a wrench for those bikes without quick releases. You should also check the tire for wear.
Check your brakes: both front and rear brakes should be in good working order. Most modern brakes have adjusters in the lever to increase the braking power as the brake wears. Never ride with worn out brakes. I carry a multitool that includes allen wrenches that can be used to make adjustments.
Check your chain, cassette, and crank. Your chain should be properly lubed and clean. Without lube your chain will not move properly, can rust, and jam. Too much lube and it becomes a dirt magnet. Too much dirt and the chain will not shift properly, and may cause "chain suck" where it fails to properly come off the flywheel. Depending on weather conditions, I clean my chain everyone one to two weeks. This can be as simply as wiping it down with a rag. I also carry a chain breaker and a few quick links.
It is good to teach new riders to deliberately go over a quick ABC check of their bike. After a while, it becomes instinctive. Walk up to a bike, give it a quick look over, squeeze the tires, squeeze the brake lever, and go.
The ABC Quick Check, NHTSA (crediting the League of American Bicyclists); Basic
Bike Check, League of American Bicyclists; ABC
Quick Check, Bike Collective.