what is the quickest way of accumulating wealth

The quickest must be the lottery,  but of course you never asked about
odds, chance or risk.

Retirement money:
Many companies/governments match part of your retirement funding. 
This matching in addition to large contributions growing compoundly
over time can amass great wealth.

Let's assume you make $60,000, your company matches 5% of your income
into your retirement account, you invest alot (25% of your income...
which can all be tax deductible in a 401K and IRA) and you make a 12%
rate of return in your aggressive retirement account, and you get a 6%
raise every year.
You invest $15,000 per year (25% of $60,000) and your company matches
$3,000.  That's a total of $18,000 the first year and this amount
rises 6% every year.

In 15 years you will have $1,000,000
In 20 years you will have $2,200,000
In 25 years you will have $4,400,000

Also remember that this is all tax deductible when you put it in... so
you will be saving about $5,000 in taxes your first year (and more as
your income goes up).  Currently the IRA maximum contribution is
$4,000 per year and the 401K is $15,000.  The IRA is scheduled to
increase to $5,000 in 2008 and the 401K is scheduled to increase with
inflation (approximately $500 per year is my guess).

The Kelly criterion (bet a percentage of your total wealth equal to
your percentage advantage in the game) will accumulate wealth faster
than any other rule, but this is not necessarily optimal for normal
risk aversion fucnctions.