I don't carry a wallet for two good reasons. First, it prevents having my entire life stolen by a pickpocket. Second, I never carry around enough to make carrying a wallet worthwhile.
Anyway, what I'm carrying depends on what I'm doing. For a quick trip to a local store, I just carry enough cash to buy whatever it is I'm buying. No ID, no credit cards. If I'm traveling on the subway, I'll carry my Metrocard, a credit card, an ATM card, sometimes my State ID card, and a little cash. I never carry over $20 cash. If I need more, I can always go to an ATM, and I use credit cards for large purchases anyway. When I ride my bike, I'll carry my ID card and a little cash. As you can see, there are never any circumstances that would warrant carrying a wallet. I like to travel light. In addition to the items mentioned, the only other things I carry are my keys, a comb (sometimes), tissues (sometimes), and maybe a camera if I'm going anywhere worth taking pictures. The less of my life I'm carrying around the better in case I'm kidnapped or arrested. No need to give anybody who might want to harm me an unfair advantage.