It's wise to keep some cash on hand at all times, just in case. Find a place you can stash it safely out of the way and where you won't accidentally spend it on a non-critical expenditure. Cash can get you out of a jam all over the world - buy yourself a ride, repairs, fuel, food, water, a place to sleep, etc. My emergency cash stash has saved my bacon several times.
Amounts will vary - I generally carry $125, folded up neatly inside my wallet. I've heard about others who carry $500 or $1000 in cash, at least when travelling. Whatever amount you decide on, make sure at least some of your cash stash is in smaller denomination bills - $5s, $10s or $20s. In normal times, some establishments will not accept larger bills, and certainly don't expect to get change of any kind in an emergency.