I have two supplies of cash with me. I generally keep about $200 in twenties in one section of my neck wallet (I prefer using this over a moneybelt, extra pocket or leg wallet). It's for emergencies. Normally when I get home, it's still there.
I'll get euros from an ATM. Typically, I'll keep euros in two places. In one of my front pockets, I'll carry a day's petty cash, generally no more than 50 euros, in tens. Most stores frown when they see a 20-euro bill or higher, especially if you're purchasing morning coffee and taking all their change. I'll also keep a supply in my neck wallet (maybe another 200-250 euros) for future days and recharge as necessary.
Most of the time, a decent credit card is better than carrying cash. Occasionally, a small business or street vendor will want cash (probably more so in Italy than in Scandinavia) so I carry some. I keep a credit card in one of my front pockets and extra cards (different accounts, not extra cards for the same account) in my neck wallet.
I don't keep anything in my pockets I'd be overly worried about losing. Anything I'd worry about goes in the neck wallet. I seriously avoid getting into my neck wallet in public.