The Millennium Falcon has changed hands several times. In the Star Wars film saga, we mainly see it being used by small crews for clandestine purposes: smuggling, rescuing princesses, and destroying Death Stars.
In normal commercial operation, how many crew members would a YT-1300 light freighter like the Millennium Falcon have?
Per an image DVK posted in another answer of his, the Falcon "sleeps 7".
(There are two rooms with triple bunks in them, and there's an additional bunk next to the lounge seat.)
However, we all know that a tent that "sleeps N" will only fit N - x actual human adults, where x is between 2 and N-1. The same seems to be true of the Falcon, because -- as the schematic also shows -- there are only 4 vacuum suits provided, and more critically, only 5 oxygen masks.
It's possible that the vacuum suits are for EVA work, rather than emergencies, so there is no need to provide one for every crew member. However, it seems to me that on a spaceship, oxygen masks serve the same function as life preservers on boats: in the event of an emergency, they provide a little bit of life support. (In both cases, the cold will kill you before the lack of oxygen/buoyancy will, but let's not talk about such morbid things.)
So, at least according to this schematic, the maximum crew complement of the Falcon is 5, at least for a responsible captain; an irresponsible captain (whose crew is not up to date on the specifications of the ship, and/or breathes something other than oxygen anyway) can employ as many as 6 people, for a total crew of 7. The Force Awakens showed that the minimum required to fly it is 2, because there are vital controls that you can't reach from the pilot's seat.
Based on the Falcon's schematics, it would be between 2 and 6 depending on mission profile:
Can't be more than 6. Falcon's schematics show two 3-bunk rooms. And more importantly, only one head.
Can't be less than 2.
The Force Awakens clearly shows (especially novelization text) that 1 person simply can't operate the Falcon - you can't even reach the shield controls from Pilot seat (which is why Rey's initial maneuvers on Jakku were so weird - she was trying to reach while flying)
The Force Awakens Incredible Cross-Sections page 35 says Falcon's crew minimum is 2
If money is no object, 4 people for a possibly-risky mission seems the minimum: Pilot, Copilot, and 2 people to man the top and bottom turrets. TFA Incredible cross-sections page 35 shows "Engineering Station"; which means an intended full complement includes an engineer, which makes properly crewed ship would have 5 or 6 crew.
The Millennium Falcon Owners Workshop Manual shows the Falcon as being a YT-1300f (the dedicated freight variant, others are the passenger transport YT-1300p, and YT-1300fp which is a mix of the two). For all variants of the YT-1300 the listed crew complement is two, however the number of passengers varies from model to model - for the f and fp models 6 passengers can be carried, the p version carries 9-15 passengers.
A quick note to people counting either beds or seats, that will likely lead you to the wrong conclusion.
If you applied that to a nuclear submarine, you would drastically underestimate the number of crew, because people work shifts and share bunks (US navy terminology is hot bunking).
So there are minimum 3 pilots, rotating between
Pilot's Chair Co-pilot's chair bed 1
There will be 2 gunners, but these are unlikely to spend more than a few hours a week in the gunnery chairs. They will share bed 2, but otherwise mess about playing that chesslike game when the ship is not under attack. Only 2 are needed, not 3 because they only have to pay attention so infrequently, unlike pilots who must both be at the wheel at all times in a ship that obeys regulations.
I would suggest there is likely to be 2 engineers as well, who can share bed 3. This will allow someone to always be manning the engine room, as well 8 man hours per day for repairs (16 hour work days).
This leaves us with 3 additional bunks in 1 room.
Depending on how these are hot bunked, they could support 1 selfish captain, 3 passengers in relative comfort, or up to 9 crew if they were required.
The Falcon, obeying sensible precautions, would host 8-16 people at all times.
In Star Wars: The Old Republic, smuggler characters get a Corellian as their home ship. By the end of the game you have 5 permanent companions living on the ship with you (plus a protocol driod). Each has their own room on the ship they hang out in. There are currently ways to acquire 2 more, but I've never done that so I don't know if they have places on the ship as well.
That makes this somewhat consistent with the other blueprint-based answers that have the upper limit in the vicinity of 5-7 crew.
I doubt this is canon of course, but a lot of the details in the blueprint in those other answers probably isn't canon anymore either.
In Return of the Jedi there are two soldiers doing nearly nothing during the Battle of Endor behind Lando and Nien Nunb. Nevertheless, Lando seemed to feel the need to staff those two seats so they must of had some purpose. Since it was a intense battle I can't imagine they didn't also have two gunners - though we don't really see those guns firings. Lets assume those guns were staffed.
So for a combat mission I would say the minimum ideal staffing would be 6 people with each person having a very specific purpose. For a non-combat mission such a crew would be wasteful (salaries, food, crowding, etc) and the crew would each serve a broader set of duties.
The gunner, for example, would only be a gunner for a few rare moments they are in a pinch and spends most of his time attending to the cargo, serving as a navigator, cleaning the head, or otherwise. It would be pretty dumb to drag a rarely used gunner around the galaxy just to sit around and play holochess most of the time.
In various Star Wars scenes it is almost always "all hands on deck" when there is a crisis so I can not imagine how just Han and Chewie can stay alive (lucky, I guess) when its just the two of them - clearly that is not enough. If you asked Han it would be three. Notice how he offered Rey a job but not Finn (he also offered Luke a job in Episode IV, 'member?).
So Han views the ideal crew as three for general smuggling operations while Lando would say six is the ideal crew for a battle.
