On average, Is there a set number of years you must work before one can retire?

In the US, many people plan retirement around starting their Social Security payments.
Those payments are based on how much you paid into the system over 35 years of working. If you work less than 35 years, you have some zeros in that calculation, so you'll get less out. 
You also cannot take Social Security before age 62. Similarly there are tax-free accounts for retirement savings that you cannot withdraw from until age 59.

But if you don't need these sources of money - for example, if you inherit ten million dollars - you can retire at any age.

Nope. I retired at 59 after working 8 different jobs.
My suggestion is to find jobs that offer a "pension", get vested, then change jobs to provide maximum security (I learned this later in life). I now have 5 sources of income.

Generally it is ~ 66 or when you can collect SS but if you have >$2M you are OK if you invest it. $5M if you wish to travel.

No. Sometimes there's a legal or negotiated age, and for certain jobs - the ones tough on your body - unions are trying to negotiate a number of years. For instance, for construction-workers - most of those lose the ability to do the job years before reaching 65

It all depends on the standard of living you wish to enjoy and how long you wish to enjoy it.  For instance, in 1968 (the best time for the working middle class in the post-war era) the life expectancy was about 70 years and the normal retirement age was 65, though people could retire earlier if they had enough put away.  But even then, the idea was that a person would only be retired for 5 to 10 years before they croaked.

So if we keep that mentality, with life expectancy at 78, we should retire at around 67 to 68, which means that if you start working at 18, that's 50 years of working.  Jesus...that's depressing.

Until recently the State Pension age was 65 for men and 60 for women.
Starting work at say 20 that would mean 45 years for men and 40 for women.
However, the age at which you can claim the State Pension is gradually increasing and is set to rise to 67 for both men and women by 2028.
A person may start work earlier, (such as 16), or much later, (35 perhaps).
If a person contributes to a private pension he/she might choose to retire earlier,
(55 for example), or could be made unemployed or redundant unwillingly.
Alternatively, some people work on beyond 60 or 65 either by choice or because of financial necessity. Another option is continued work but with lighter duties or on a part time basis.
So there is no single answer; but perhaps retiring at 60 or 65 is more usual.

I don't think there is a must aspect to it.  there is an opportunity.  Somewhere on the order of 40 years is the general idea.  Lots of people are still broke though after that and can't really afford to retire.

That depends on your vocation.  In most states cops can retire after 20 years and get a pension of 1/2 their salary, or they can stick around for another 10 (30 years total) and get 3/4 salary.  ---  Similarly for firemen.  Teachers must have at least 30 years and have to be 55 years old r more to get 1/2 their salary.  Judges must be elected for 2 terms (6years each) and they get 60% retirement.  ===  Large corporations used to have pension plans, but most of those have been taken over by their unions.  Those plans (either by the corporation or the union) are bad.  Basically they expect you to work until you die. == Maybe yu get a retirement at 67 if you haven't been laid off from the factory.  --  Most other places -- like Walmart -- expect you to provide your own retirement thru savings or a "401k" plan.  For this you put money into the 'plan' and whatever interest or dividends it gives provides for your retirement.  If you make a bad investment you can LOSE a lot of the retirement money and have nothing left to retire on.  For those plans there is a min age usually 59 and 1/2 years old.  If you have nothing else and you have worked enough there is always Social Security,  women can retire at about 63 for a reduced amount and at 67 for a full retirement -- men can retire at 64(?) for a partial and 67 for ful retirement the amount depends on your salary. = = =  You can see that there is no real set or even average retirement age.