Debit cards. Cash burns a hole in my pocket and is way too hard to deal with. Plus it's filthy and bulky. I also use mint to keep track of where my money goes (strict budgets) and cards make that easy. Yes, I'm a certified control freak.
The only time I use cash is at the farmers' market and getting quarters for laundry.
I pay everything I can with a credit card because I have a capital one cash back credit card. I pay it off immediately and NEVER carry a balance. I write each transaction out of my checkbook immediately like I would a debit card, and never buy anything I couldn't afford to pay right that second.
I prefer to pay with cash. I find it's easier to keep track of your expenses if you can actually see the money exchange hands. If it's just a piece of plastic which is handed back to you then you can get carried away.
I put everything I can on my credit card; it's just so much easier for me. Putting everything on that card allows me to view in real time everything I've purchased, and check across my receipts that all of the figures are correct. I prefer it to cash because I earn money back through it, and since I don't carry a balance from month to month there's no harm being done to me or my credit line.