Spokes should be kept clean. Put a drop of oil on the end of each one every once in awhile.
A small dent in the rim of a wheel can easily be straightened with an adjustable wrench. However if it is a big dent, you will have to get a new rim. The braking pads will wear the braking surface of the rim. This will cause a deep ridge to be formed all around the rim. If you are able to flex the rim in with your fingers when the tyre is not inflated, the rim needs to be replaced.
Hubs should be kept clean and well greased. If there is any play in the bearings, it needs to be tightened immediately. Check for play by rotating the axle and trying to move it from side to side.
Tyre tread should be checked regularly for wear. A worn tyre is more likely to get a puncture.
Hub bearings should be checked for wear by lifting the wheels off the ground and spinning them. It is a sign that the bearings are worn if you feel a vibration coming up through the handlebars.
Tyres should be checked for thorns, pieces of glass and wire. Keep them pumped up to the correct pressure. Check that the rim of the wheel does not have any sharp edges and that the rim tape is properly installed. After installing the tyre make sure that the brakes clear the sidewall properly. If the pads are rubbing against the tyre you will hear a scuffing sound.