I, too, have a few cards that are always at zero balance. I've got about nine credit cards right now if my memory is correct (I didn't go through my files). None of them are store-issued cards that can only be used at specific stores, although some are Visa or MasterCards issued in partnership with certain retailers so a discount or extra points apply when shopping at those businesses. I pay off all my cards immediately so I do not pay interest on any of them, and each card has a specific purpose intended to maximize my savings or rebates.
With one card, I get free shipping, monogramming, and $10 coupons for my favorite clothing and outdoors retailer. With another, I get twice the rebate points when shopping at the chain (also an outdoors retailer) and I can either cash in the annual check or use it for gear. Yet another card is through a national horse breeders association, and it offers a great annual cash-back program as well as specific discounts on horse-related goods and services (which I'm prone to use quite a bit). One card is an AmEx -- specifically so I can get cash back on CostCo purchases. There are three generic cash-rebate cards, one for my business and two that I use regularly. Finally, there's a card on my husband's credit card account that I use if I'm picking something up for him -- we keep our finances largely separate.
One advantage to multiple cards is that if I sign up for the quarterly "bonus savings" programs, I will nearly always have one card with double points back on grocery stores or gas, another that has double points back on hardware stores, and so forth. I routinely sign up for those extra savings, and I make a note that I carry with each card to remind me which one to use for those purchases for the quarter.
I get a considerable amount of money back every year in cash rebates. I'm a big believer that credit cards make wise financial sense as long as they're paid in full, on time, every month -- and as long as the carrier has the discipline to avoid impulse purchases just because they have a high enough limit on their cards.