Broken Chain - If you have a chain breaker push the damaged pin out and re-connect your chain at the next sound link. Shortening the chain might make it difficult to ride in the big ring in and big cog in the rear. If you don't have a chain tool, you might have to improvise by using a fist-size rock. Yes, it does sound primitive but effective if your ten miles away from anything. The best process for this method would be to place the backside of the loose link onto a similar-sized rock then pound the pin in with the rock in your hand, if this works be very gentle riding back to your car. Whenever a chain breaks you should replace your chain before your next ride!
Bent Rim - If the rim is slightly bent it can rub on your brake pads, frame, or chainstays. First, try to loosen the brakes or release the straddle cable. If you have a spoke wrench use the brakes as a guide and tighten/loosen the spokes. If your wheel is bent side to side, first you are going to have to release the brake and remove the wheel from the frame. Check for broken spokes and try to remove any if possible to keep them out of the way. You can also twist them around the next good spoke. Try to place your bent wheel against a tree holding the bent sides, then with a few quick jolts try to bend the wheel back to a ridable state. This process may have to be repeated a few times depending on the condition of the wheel.
Bent Chainrings - Your crescent wrench out of your tool kit is going to be the best tool for the job in this case. Place the tool over the part of the ring that is bent, making sure it clears the teeth of the chainring, keeping them from snapping off. Once you have the wrench in the proper position, push or pull the bent part very gently to try and realign the ring back to its normal position.
If it is unrepairable put the chain in the middle chainring and just use your lower and middle ring until the upper ring can be replaced. Check the bottom bracket before you come to the conclusion that your chainring is bent, because you may have also damaged the bottom brackets spindle. A badly damaged spindle means that you will be walking home.
Chain Suck - If you do get chain suck on a ride stop pedaling and get off the bike In most cases you should be able to grab the chain and pull it back the same way it sucked up. You may have to use a little force or roll the bike backward while pulling the chain.
If it is still stuck you may have to detach the chain from the bike with the chain tool, then re-route the chain back through the drive train. Check for any kinks or twists in the chain before you install it back on your bike. This can cause problems in shifting if not checked before installation.
Broken Derailleur Cable - If your derailleur cable breaks while you are on the trail, you will still be able to get home, but only in a fixed gear. When this happens you need to put your chain in the desired gear that fits the terrain you are riding and screw the high/low adjustment screws until the derailleur is lined up with that particular cog.
The spring tension on the derailleur allows you to lock your bike into a single gear. For the front derailleur adjust the low adjustment screw into the desired chainring positioning so that it will hold it in that spot.
Broken Derailleur - You can convert your bike to a single fixed bike if the derailleur has broken. First, remove the chain and then remove the derailleur with a 5mm Allen wrench. Place your chain in the middle chainring in the front and the middle cog in the rear. Using your chain tool, remove as many links until the chain is as snug as it can get around the drive train.
Loose Crank Arm - A one key crank bolt is an Allen bolt that threads through a special cap and on into the end of the spindle. With a one key crank bolt, you can tighten your cranks with a 5mm Allen wrench. Additionally, a one key crank bolt also works as a crank puller. Since the bolt is not flush to the crank arm it does require frequent tightening.
If you have standard 14mm crank bolts and you don't have a 14mm crank wrench with you take a small crescent wrench spin the bolt tighter. To facilitate getting the bolt tight, you might want to pound on the crank arm with a rock. The further you can get the crank arm onto the spindle the longer it will stay in place. Be careful when using a rock on your cranks, they will damage easily.
Loose Headset - If you have a threadless headset follow the detailed instructions. If you do not have a compact headset wrench you will have to use your hands to cinch down your headset. Grab the top of the headset and twist the locknut clockwise. Hold the front brake and wiggle the front end and try to tighten. You may have to stop and do the same process over and over again.
Torn Tire Sidewall - The standard way of fixing a slashed or torn sidewall would be to place something inside the tire in between the tube and the sidewall to keep the tube in and the elements out. Place the material inside the tire carefully so that it will stay in place while you inflate the tire. I have known of people using a folded over dollar, power bar wrapper, sandpaper from your patch kit, or the large patch out of your patch kit. Gray duct tape is the best solution, wrap some tape around your tire lever.