Well tape and CD players will require the standard cleaning and checking that most other equipment requires from time to time. However, you need to be careful not to put the loading/playing mechanisms out of alignment, as this can cause problems.
The general steps have been covered in several posts on this site but to quickly cover
1. Unplug the unit
from the mains
2. Check the plug
, cable and any external sockets, switches, knobs etc
3. Open the unit
up and remove any dust and other dirt with a paintbrush and a vacume cleaner
4. Check the boards for obvious damage, burned components, blackened sections on the board, dry solder joints, capacitors that are showing signs of heat stress etc
5. look at any rubber belts or rollers for signs of wear or damage.
6. If there is any damage or wear, get the unit
looked at by a service tech
7. Clean the heads/laser
optics with a cotton bud and (read just damp with) isopropyl alcohol. Allow it to dry completely before using the unit
8. Spray the pots and switches with a lubricating contact cleaner
9. Put it back together and test it.
Most of the problems that I have had over the years with tape/CD decks is dust in the pots (the scratchy sound when using them), worn belts and pinch rollers or worn audio heads and mechanisms that become disaligned. Keeping the units clean will go a long way and it is something that you should do every 6 months to a year, depending on use. Also, covering them up when not in use will help keep dust out.
As with all things - if you don't know what you are doing, leave the repairst to those who do. Howver, the general cleaning and checking should be something that you can do, even if you don't feel confident about the other things.
Hope this is what you are after. Also remember to do a search on service or maintinence within the fora for more info.