Etched rubber, the kind used to make your beautiful rubberstamps, can last decades and be passed down from generation to generation. For general rubberstamp care, or for precious rubberstamp collections and for rubberstamp heirlooms that will last and last, I recommend...

• NEVER store rubberstamps in the hot garage or other rooms in the house with extremes of temperature like a seldom-heated, cold storage room. Rubber likes being stored in the same temperatures you like living in, at room temperature, around 70 degrees. If you like your house at 68, that's fine. I like it cold, too, and my stamps have lasted! If you have to shut off the air conditioner to save $ so you can buy stamps (well, okay, groceries!), that's fine, too, just do what you can to keep the house at a comfortable temperature. Consider weather stripping doors and windows with cost effective kits from the hardware store, and make other cost effective energy improvements when you can, lilke better appliances and energy efficient light bulbs. Your electric company can suggest changes to make your home more energy efficient. Then spend your savings on craft supplies and art classes. Screw the kids and their college education.
• PAPER OR PLASTIC, MISS? ... DO STORE rubberstamps rubber down. Rubber oxidizes when exposed to air. Ever get chapped lips in the wind? This can happen to rubber from air molecules over time. So do store your stamps rubber side down. Ideally, store them in plastic trays or on top of plastic, which creates a seal and minimizes air exposure. Many rubberstamp companies sell rubberstamp sets in a thin plastic tray or box. Keep the box and store them in it. For large sets where it gets confusing what sets or what empty spaces used stamps go back into, stamp white paper to show where stamps go back, and place or tape the stamped guide underneath the tray, so the rubber is in contact with plastic, not paper. Page protectors are too thin a plastic and don't really stop the oxidation; over time even a simple printout will bleach into a page protector. You can try it for awhile, but upgrade to thicker plastic when you can. Not contact paper; that stuff is vinyl and adhesive; ever smell it? It lets off a noxious gas. I can only imagine what it's doing to stamps. I guess it would be okay in a pinch, but eventually do try to upgrade to something better, so you can be a true rubberstamp snob. Okay, okay, there does come a point when OCD takes over common sense over this issue. I store my stamps on wooden shelves, where I can categorize and see them. Some are in trays, but many are not. I dust them once in awhile. They've lasted me quite awhile and they're doing just fine. They've been inside a hot cargo box on a boat sailing from the US to Japan and back, for my military service, and been fine. Eventually I plan to construct a true craft room with trays for my stamps and papers, and places for all my ribbon, but for now, they seem to be happy with how they've been treated; never in the garage, and always inside with me when I could help it. Never left in a hot car overnight; always brought promptly back inside after a class.
•  If you have little ones or a puppy in the house, or have a dog who likes to chew, put something in front of your stamp storage where they can't get to it. Luckily, my neighbor was a caring woman who replaced the stamp her two year old ripped apart, but I doubt your german shephard is going to be able to reconstruct your priceless scrapbook. Take a moment and keep your adored craft supplies and creations out of their reach!
• NEVER clean rubber with baby wipes. Some baby wipes contain forms of lotion, that chemically are in the same family as oil or grease, and this can cause rubber to oxidize and break down. Remember the warning on the side of the Trojan box? The same is true for rubberstamps. Grease, oil, vaseline, lanolin, it all causes a form of rust, that attacks rubber. Use a water based rubberstamp conditioner specially formulated for rubberstamps, or just water on a papertowl.
• NEVER run stamps under running water, even large stamps. The adhesive between the rubber and cushion and wood, and the wood itself, are organic substances, and in effect, alive. They will soak up water, expand, and the chemical bonds will break down over time. Don't soak stamps, either.
• Invest in a rubberstamp scrubber. The fibers are really soft, and dense, and clean stamps really well, even line stamps or stamps covered in embossing ink.
• For archival ink, that is really black and tends to stain rubber, it's acid free, and it's okay to leave it on the stamp, but, if you really want your stamp as clean as it could be, you can try Simple Green. It's pine based and I've had rubberstamp instructors who had success with it, and it didn't degrade their stamps.  
• New rubberstamps fresh from the store or factory have a bit of rubber dust still on them, from the manufacturing process. Pre-condition new rubberstamps by inking them then stamping on a brown paper grocery bag. The brown paper is really fiberous, and soaks up that powder really well. Repeat a few times. Thereafter, your stamps will ink properly and give you beautiful images in your projects. This is especially true of solid image stamps, ones that stamp all color and very few outlines.
• Clean stamps right away. Embossing ink that's had days to dry, crack and sink in, will clean up harder than ink that's only had minutes to a couple hours to set in. Clean up as soon as you are done being creative for the day. Wrap up creative time a little earlier to leave time for clean up. You'll enjoy your crafting time more, get to sleep on time, and you'll always enjoy starting with a clean play area each time. Your creative juices will flow more regularly with adequate sleep, so take the time to clean up, and respect your body's needs while you're caring for your rubber treasures. End your day on a good note.   

If you have any questions, ask!