Stamps are pretty hard wearing parts of your craft supplies arsenal but if they will wear out if you don't take proper care of them.
To keep them in tip top condition, then you need to keep them clean, dry and out of heat and sunlight. My stamps are made from a light sensitive polymer so if you keep them in bright sunlight then they will degrade. And heat will melt them so no leaving them on a sunny desk. Keep them in an opaque storage box if you can.
To clean them up, you need to get the right king of cleaner for your ink. If you're using a permanent dye ink (like Stazon) then you will be best off using a specialist stamp cleaner as this type of ink can damage the surface of your stamp if you leave it long enough. If you're using a pigment ink (like the Crafters colorbox or Versacolor brands I stock) then simple soap and water is what you need. And the only useful thing you could keep around would be an old tootbrush or soft nail brush. See below for the difference you get with cleaning techniques.
Stamp cleaned with a cloth
Stamp cleaned with a soft nail brush
The difference in cleaning makes a huge difference. And whilst running them under water won't do them any harm, don't leave them soaking in water as they will absorb it and start to swell, and we don't want that! Just make sure you let them dry fully before putting them in your storage box and your stamps will give you many years of crisp printing. They can do over a million impressions if you treat them right!