Most modern airliners require two pilots to operate. Older airliners require a flight crew of three: two pilots plus one flight engineer.
Has there ever been an aircraft where the number of required flight crew members is extraordinarily high, for example five or six?
To clarify the question:
"required flight crew member" is the number required by relevant regulations, not the number needed to physically operate the plane. If that number is not met, the plane could not legally have taken off
gunners / weapon operators of military aircraft who are not necessary for a safe flight are not included
In addition to the An-225, a few historic examples at five, a couple at six, and one (possibly) at seven.
I don't know how firmly worded regulations were at the time so I can't speak as to whether all of them were absolutely required to be in place for takeoff. As neither of the six-crew airliners entered service, the question might be moot for them anyway.
At least one operational airliner had a minimum of five -
The Boeing 314 had a flight crew of five - two pilots, a navigator, a radio operator, and a mechanic. However, for the intended long-duration flights, it apparently carried two full crews plus two additional people - a chief engineer and a clerk. Relief crew are probably outside the scope of your question, but it's not clear to me if the two additional crew would have been "required" even for a shorter flight (the engineer maybe, the clerk probably not) - so the answer might be six.
And some military aircraft with five or more -
The Zeppelin-Staaken R.VIapparently had a flight crew of seven (commander, pilot, copilot, radio operator, fuel engineer, and two engine mechanics) - I say apparently because that list doesn't seem to mention gunners. There may have been some duplication of roles.
The Linke-Hofmann R.I (did not enter service) appears to have had a flight crew of six, but the details are sketchy.
I think the basic "flying" crew of the B-36 was five, after taking out everyone with a combat duty - two pilots, one engineers, radio operator & navigator; see this list - but it's hard to break out the exact roles and determine who was there for relief purposes. The XC-99 cargo variant also had a crew of five, which seems consistent with this.
The Me 323 transport had a crew of five not counting gunners (two pilots, two flight engineers, radio operator)
While only one was built, plus two copies which were built in Italy, the Dornier DO-X with twelve engines, is listed as having a flight crew of 10 to 14 during normal operation. Twelve of the relatively high maintenance engines of that era must have been a handful to keep operational during flights.