1) if very few people have more than spare change in their pockets, criminals have less incentive to rob people.
2) no trips to ATMs/banks to refill cash supply
3) sales tax gets paid 100% of the time (no under the table deals)
4) Receipt trail (a card number can be used to look up a lost receipt, no such luck for cash), so I can always get proof of warranty later if i loose a receipt, and return things without one too.
5) I pay the same price either way, but i get points using the card, extended warranties, theft protection, and I can stop payment if I think I git screwed or they refuse a product return.
6) lost card != lost money (especially most that have fraud/theft protections on plastic too)
7) Merchant can't be given counterfeit money (and even fraudulent transactions are guaranteed to be paid to him if Visa approved it).
8) No "crap, i don't have enough cash on me" moments what waste time and turn into no-sale with customers (and also no "sorry you made that pizza, but i only have $5, so, throw it out I guess." moments either)
9) Merchant can't get robbed for as big a loss since less cash is on hand.
10) less time counting down the till, and less mistakes too.
11) harder for cashiers to pocket a transaction instead of ringing it through. (charge customer cash, cancel transaction at last second, pocket money, no longer possible).
12) costs the same, roughly, as processing a check, but is more secure and comes with guarantees for the merchant.
I can easily go on.