I have always used baby wipes to clean my red rubber and clear stamps. They have a little lanolin in them and this keeps them soft. I like the generic ones. Some of the high dollar brand-name wipes tend to leave lint on the stamps. Baby wipes are usually alcohol-free and this is what you want. Alcohol can dry your stamps. This might not be a big deal if you live in a humid part of the country, but if you live in the desert any alcohol applied to your stamps can be a problem--your stamps will get a white ashy look and eventually will crack. I lived in the desert and had to condition my stamps (clean with veggie oil--see below) at least once a year.
If you have a stamp that is really dirty and won't come clean with wipes, take an old toothbrush (soft) and dip it in some vegetable oil and scrub it. Then spray it with an off the shelf stamp cleaner to remove the oily residue and wipe with a baby wipe. Make sure you get all the oil off or the stamp will get sticky.
A stamp scrubby pad works well to keep stuff from building up in the grooves of your stamps.
I had at one time around 5000 wood mount stamps. About a year ago I sold about two-thirds of them. They were all in very good condition and were like new. In fact, everyone commented on how well taken care of they were.
As far as the foam stamps go, it depends on what you are stamping. If you are using paint to stamp with your foam stamps then soap and water work best. If you are using ink, you can still clean with baby wipes, but you will probably find that the foam absorbs quite a bit of the ink and it penetrates deep into the foam, thus making it harder to remove all the ink. This is why I have always preferred the red rubber mounted on wood. Foam stamps are generally best for stamping with paint, while rubber and clear polymer stamps are good for ink.
This tip was shared by Scrapbook.com member and avid stamper heidimansi.