The plastics used in the cases of most electronics are magnets for dirt and crud of various sorts. Clean cases, keyboards, and controllers are not only more pleasant to use than dirty ones, they also result in less destructive dirt getting into the working parts. Clean working parts mean longer life and better operation than dirty ones.
Unplug everything, especially power, before cleaning. Keep the power plug somewhere where it can't be accidentally plugged in while you're cleaning. Never use cleaning solvents on a piece of equipment that has power applied.
Do Dry Cleaning First
Clean away as much dust, hair, and other material as possible without using a cleaning solvent first. Use folded corners of paper towels, small brushes with stiff bristles (toothbrushes or acid brushes, for example), and cotten swabs to get into tight areas. Be careful not to use too much force when cleaning in these tight areas, you don't want to break anything inside.
Test the Cleaner Before Use
Plastics come in many varieties, and different cleaning solvents have different effects on them. Before using any cleaning solution, test a small amount of it on some part of the equipment where it won't ruin it completely if it decides to dissolve the plastic. Many common household cleaners are now marked as to whether they are safe to use on plastics. That's a good place to start, but you should still test a small amount of the cleaner on the equipment, since something that's safe for fiberglass shower stalls may not be safe for the polystyrene case of your equipment.
Spray the Rag, Not the Equipment
When applying cleaning agents, apply them to the cleaning rag, paper towel, or whatever you are using to clean with, rather than spraying them directly onto the equipment. This will keep the cleaning material from getting inside the case, or on to parts of the equipment where it shouldn't be.
Keep Liquid Off Contacts
Don't put household cleaning agents on metal contacts, such as the connectors for controllers or for cartridges. General household cleaners can cause corrosion of these contacts. Clean these contacts with isopropyl alcohol if you feel the need to use a solvent. Otherwise, just clean the contacts by wiping them while dry.
Copper "fingers", that is, copper lines on a circuit board, can be cleaned using a clean pencil eraser. Don't try to use an eraser on "leaves", that is, copper strips of metal that are not directly on a circuit board but are loose in the center. Also, don't use an eraser on pins. Atari 2600 and 7800 cartridges have fingers on them, for many you'll have to push in the cover on the end of the cartridge to see the fingers. Other cartridges have the fingers exposed. The socket in which the cartridge goes has leaves, however, and you shouldn't push anything into the part of the socket where the copper leaves are, since it may result in bending or otherwise damaging the leaves. The plastic part of the socket is safe to clean by wiping, however.
Using Older Equipment
Careful use of your older equipment will keep it working for a long time. When equipment goes bad, it's often because of some specific event that causes damage, rather than as a result of simply aging. There are parts of the equipment that are subject to the effects of age and regular use, but with care the life of these parts can be extended.
Count to 10
Whenever you turn power off count to 10 before you turn power back on again, or connect or disconnect cables, controllers, or cartridges. Fast power cycling, making or breaking connections while residual charges are still present can cause electronic damage to the equipment.
Hold the Connector
When handling cables, such as when plugging in controllers or power cables, hold the cable by the connector, not by the cable. The specific part of the connector that is made to be held is called the backshell, and it will usually have some texturing to provide a good grip.
Also, when plugging into the wall or unplugging, don't yank the cable. We all know better, right?
Don't stretch out cables into clotheslines when you're using them. Power cables should be long enough to allow the cable to rest on the floor or some other surface between the wall plug and the equipment. Controller cables should also be long enough to allow them to rest on a surface somewhere along their length between the equipment and the player's hands. If the cable is hanging on nothing but air between the plug and the player you're putting unnecessary stress on the cable that will probably result in damage to the cable, and possibly damage to the connector on the equipment.
Careful with That Connector
Don't use excessive force when connecting things to the equipment. Probably the most common damage I see on old equipment that is either not working or acting flakey is cracked electrical connections on the connectors for the controllers. This usually results from too much force being used to insert the connector in the port, or from clotheslined cables, or somebody yanking on a clotheslined cable.
If the connector is taking a lot of force to insert, chances are there's something wrong you should deal with. It may be bent pins (which will only get worse if you force the connector in), or a connector that isn't quite the right size for the port. Figure out what's hanging things up and fix it, rather than forcing the connector to take it when you ram the cable connectors into the port.
Use Extensions to Prolong Life
One way to reduce the need to put force on connections on the equipment is to use extension cables for controllers and on other connections, then plugging into those routinely instead of plugging directly into the equipment. That way you're not putting the stress of plugging into the connectors that are connected to the equipment's printed circuit board every time you change controllers.
Put It in a Safe Place
Provide someplace for the equipment to sit that gives it adequate airflow, provides it with protection from having things dropped or spilled on it both when it's in use and out of use, and allows people to walk by without dodging cables.
It may be faster and easier to lean the unit on top of a precariously balanced pile of stuff in front of the TV right under the shelf where you set your soda glasses, with the controller cables stretched across the walkway between the rest of the house and the kitchen, but a single mishap could mean "Game Over" for your classic videogame system. Take a little care, and use a little foresight, and your game will keep playing into many years of extra time.