As is very common, most forex merchants will give you your cash in the most commonly used bills. For the Euro, that would be most commonly EUR 20 and EUR 50.
If you are purchasing a huge amount of Euros, you may get bundles of EUR 100 instead.
EUR 500 bills are possible and they can look cool, although some merchants (even major ones, like hotels) may view such bills with high scrutiny or even refuse outright to accept, mainly because they are so rare and, as alluded to previously, it is a popular tactic of criminals to use higher denomination bills. Finally, unless you are purchasing a lot in one transaction, there aren't many who would like to break change for EUR 500. A bank will likely take the bill with not a problem, though some will turn their nose up at you altogether if you don't have an account with that bank.
In Swiss Francs, the highest denomination bill is CHF 1000. Large and purple in colour, it looks pretty cool. Ultimately though, it has rather limited day-to-day purpose, and most merchants probably won't accept it easily, unless you're actually buying something really expensive, like a watch. Expect that someone will check all your bills, however.
One small challenge for people who have little to no stock of USD is to somehow generate a cache of dollar bills for that said "obvious reason" which usually starts as soon as they leave the airport in the USA!
Small PSA: Remember when carrying large amounts of cash to always check the customs rules for the countries you are passing through in case you need to declare your assets over the standard threshold, e.g. in Australia, this is AUD 10,000.
