Euro Denominations at Bancomats

Most ATMs give 20 and 50 euro bills, a few will give 10 and (very rarely) 100.

Bancomats do not dispense coins or €5 notes. You can choose amounts (divisible by 10) to withdraw that will give you 10s, 20s and 50s. If you choose €200, you may get four 50s, if you choose €190 or €210, you'll get some smaller notes.

There are no €1 or €2 notes, these are coins.

More to general Europe, I have run into rare machines that allow you to pick the denomination of notes, but as others have noted, mostly 50 and 20 euro notes, some machines have 10's.

In case you have no choice of bills (most common), take an odd amount, like 260 EUR, to insure you get some smaller bills.

I buy things with my € cash, so breaking a 100 note is not too difficult. Shop keepers will tell you if they can't break it. Most meals out cost on average 30€ a person, so a restaurant is an easy place to get change. If you're someone who wishes to use credit cards all the time (if accepted), it gets a little more challenging to break the 100's.

I covet my smaller € notes. I find them more and more difficult to acquire, and I never have enough. Every chance I get, I use a 50 or a 20 to pay for smaller items just to build up my smaller bill stash.

Some machines provide change, others don't. You'll never know when having change will come in handy until you need it, and many tourists make the mistake of not being prepared. You can waste a lot of time trying to find a place to break a large bill, especially when the banks are closed.

I've never seen a machine give coins or 5s. Usually it gives 20s or 50s, sometimes 10s too.

There are no 1euro bills, 1 and 2 euros are coins. Bills are 5, 10, 20, 50, 100 and I don't know about higher than that.

FYI, Euro bills also vary in size , getting bigger as the value increases. Bills up to €100 can fit into a snack-size ziploc bag (keeps money dry in a sweaty money belt.)

But I have received a €500 bill from an ATM, and ended up having to go into a bank to break it. After that, €490 is my max withdrawal

Bancomat machines do not dispense 5€ (the smallest bill)
But banks also fill machines with very few 10€ bills, so those are dispensed sparingly as well.
The shortage of 5€ and 10€ bills are often the target of criticism toward banks, which however prefer stuffing ATMs with the larger bills because it decreases the labor costs of filling the machines.

The most common denominations issued by ATMs are 20€ and 50€ bills.
I don't remember if I ever got 100€ from the machines, but those are very common as well.

There are also 200€ notes and 500€ notes. I got them occasionally from the bank (from the cashier not the machines) when I needed to make large cash payments (especially for house repairmen, plumbers, etc.).

The European Central Bank announced they will stop printing the 500€ bill at the end of 2018, as that denomination seems to be the preferred denomination by criminal organizations for illicit payments and money laundering. If you have some left over don't worry. The old 500€ bills will continue to be valid indefinitely after the ECB stops printing them.

For some reason Americans and therefore American tourist seem to have some aversion to large bills such as $50 and that gets transferred to the 50 euro bill. We have never had a problem cashing a 50 euro note. It is common note in Europe. Occasionally I will be asked if I have something smaller. If I do fine and if I don't it gets changed. We have even used 100 euro notes with few problems. Obviously I am not using a 100 euro note for a 2 euro latte but within reason big bills are easily acceptable by most merchants. We use coins all the time and actually like the 1 and 2 euro coins. Make us supporters of eliminating our dollar bill. Would love to have a dollar or even a two dollar coin in the US. And do away with the penny.

Bills up to €100 can fit into a snack-size ziploc bag (keeps money dry in a sweaty money belt.)

I've never had anyone refuse accepting a damp banknote!