Back gear assembly (freewheel)
If your back wheel clicks or hums loudly when you coast, lay the bike on its side and drip lube into the hub of the gears. Leave the bike on its side for a while so the lube can work in. If noise persists, replace the assembly.

Brakes
Lube where the brake arms connect to the frame and each other.

Brake & Derailleur Cables
If you ride often in rain or snow, drip lube into the top openings of cable housings. Don't do this to self-lubing cables or Teflon housings.

Brake Levers
Lube the pivot points.