Depends: out and about in the US - seldom more than $50.
UK: £40-60 - usually to cover the pub bill, as running a credit card repeatedly is annoying for the barman and myself.
NZ/AU: $100, helpful on tour in remote when only eftpos/cash is fairly common.
Hong Kong: $2000. I never know when I'll "need" something or decide on a banquet.
Thailand: Depends on my itinerary, but unless I am doing a more cash only activity (intense shopping, long car ride), I found B3000 overkill most days. I found my main concern having a couple B100 notes on hand rather than how many thousands.