Check the toeing-in of your brake blocks. Brakes should work smoothly and silently. Install them so that the front edge of the brake pad is 1/32mm closer to the rim than the back edge. Oil and grease that may have built up on the rim impairs braking. Remove this with alcohol or degreaser.

Check the tyre pressure. If they are too soft, the bike will feel sluggish. If too hard the bike will vibrate. The correct pressure is on the sidewall of the tyre.

The sprockets and chain should always be kept extremely clean. Clean them after a long ride and remember to re-lubricate them. If you can lift the chain off the chain ring, the chain is almost certainly worn. This will cause the chain ring and sprockets to wear and your gear changes will be inaccurate.

If your chain jumps off the sprockets, you can try readjusting the rear derailleur from scratch. If this doesn't fix things, the chain may be too long. When the chain is on the biggest chain ring and the biggest sprocket, the rear derailleur should point roughly to the floor.

Make sure the chain ring bolts are not loose or missing. If one is missing, replace it immediately as it may cause the chain ring to bend.

Make sure the spokes are adjusted to the correct tension.

Make sure the bearings in your hubs, bottom bracket, headset and pedals are tight.

Always make sure that your seat post is well greased where it goes into the frame. It may become stuck if you do not do this regularly. 

If your seat post does become corroded and jammed in the frame, remove the bolt and use penetrating oil around the bottom of the seat post. Oil the seat post every few hours for a couple of days and the seat should move. Replace an old saddle onto the seat post so that you don't ruin the newer one while trying to move the jammed seat post. Hit the saddle with a hammer to try and move it. If this doesn't work, try turning it with a long pipe wrench.

If your brakes chatter it may be caused by a badly adjusted or loose headset. Wrap your fingers around the bottom brace and put the front brake on. If you can feel movement, the headset must be looked at. 

If pedaling produces noises from the rear of the bike that stop when you stop pedaling, the indexing on the rear derailleur may need adjustment. To fix this try turning the cable adjuster on the rear derailleur one half-turn counter clockwise.

Pedals that have bearings that grind, or bent axles, make it almost impossible to pedal. Check that the axle is straight and then check the bearings by removing the front crank.
If you remove a bolt that has had Loctite applied to it make sure you apply it again when you put the bolt back on. Loctite will leave a blue residue.