While details in this matter are not always needed in books, no hero would probably complete his journey without single coin in his/her pockets unless he would have a great deal of luck, contacts everywhere or just a bunch of questionable techniques to achieve anything.
While my thoughts in this regard were greatly inspired by games, I’ll start this chain of thoughts somewhere else: Harry Potter series, which had a few scenes featuring money: Harry’s first visit to Gringotts’ bank and seeing the stashes of gold, silver and bronze. Draco “buying” his place in quidditch team by his father gifting them Nimbus 2001 brooms. Or the moment where wizards arriving to watch quidditch world cup confuse the local landowners as they want to pay the rent for their tents with their wizarding gold coins instead of GBP or the 1000 galleon reward for winning triwizard tournament. That’s just a few.
Then there are classic mentions like endless gold pouches or just the fact that someone might get upset by losing some money while playing cards and cause a bar brawl. Pirates that tend to be out of gold just as soon as they find a place where they can get some rum.
The original plan was to use nine Pieces of Eight to bind Calypso, but when the first court met the Brethren were, to a one, skint broke. – Joshamee Gibbs, Pirates of the Caribbean: At world’s end
If things happen fast, currencies will probably not be something of an issue but in longer story arc, it could very well happen that a character (especially if he/she is driven out for any reason) will be facing the slowly drained purse in addition to any other hardship. Example could be Inheritance series where Roran is forced to pirate a ship because he (and the Carvahall refugees following him) could not pay the full journey; or the bounty on his head.
Now, full circle back to what I mentioned at first: gaming. Here and there, nostalgic people who enjoyed the hard days of World of Warcraft 1.x (not me, I started in 3.3.5) remember how even 50 gold meant something compared to days now when Blizzard implemented a huge spider mount that costs exactly 2 million gold to give the richest (in game sense) players some way to empty their pockets. The fractions below gold don’t matter any more. Same could be said about Diablo III where the lack of unit below gold causes massive inflation and after some time spent playing the game, any number lower than a million means almost nothing.
In regards to my own writing: a gladiator tournament happens in my story. By the very early phase (pre-first draft thoughts) I was working with placeholder prize money of 50000 gold (damn me for lack of specific currency name). Even in the first draft there was no mention of specific amount, only that the reward is a small fortune, especially for the main character who is on the verge of adulthood.
In that stage of pre-writing thoughts, the weapon he obtains some 10-15 years later was guesstimated to cost around 75000 because of the ingredients needed to forge the very special alloy. Another irony: while these ideas are some 10 years old, it was only a few months ago I had any specific ideas for what the ingredients will be and some weeks ago I finalized the list and still need to decide sources of some.