I'm in a kind of system that is hard to explain to people who are not from the Netherlands, as it only exists here, as far as I know... It has many benefits, but also many cons, this being one of them.
Most of my transactions are debit or credit card. I don't like to carry a large amount of cash because of the risk of loss or theft. Cards can be replaced, but cash is gone forever. But I do carry $20 or so for purchases under $5. I also keep a cash stash in a safe for things (emergency or not) that might come up. One might as well put it in one's safe considering the piddly, next to nothing interest paid on smaller savings accounts.