To simplify this expression, we can start by factoring out a -1 from each term:

(1/2 - 1) (1/3 - 1) ... (1/2008 - 1) (1/2009 - 1)
= (-1)(1 - 1/2) (-1)(1 - 1/3) ... (-1)(1 - 1/2008) (-1)(1 - 1/2009)

Next, we can simplify each term:

= (-1)(1/2)(2/2 - 1/2) (-1)(1/3)(3/3 - 1/3) ... (-1)(1/2008)(2008/2008 - 1/2008) (-1)(1/2009)(2009/2009 - 1/2009)
= (-1)(1/2)(1/2) (-1)(1/3)(2/3) ... (-1)(1/2008)(2007/2008) (-1)(1/2009)(2008/2009)

Now, we can see that each term has a common factor of -1, so we can factor it out:

= (-1)^2009 (1/2)(1/2)(1/3)(2/3) ... (1/2008)(2007/2008) (1/2009)(2008/2009)

Since (-1)^2009 = -1, we can simplify further:

= - (1/2)(1/2)(1/3)(2/3) ... (1/2008)(2007/2008) (1/2009)(2008/2009)

Now, we can see that each numerator cancels with the denominator of the next term, except for the first and last terms:

= - (1/2)(1/2009)
= - 1/4018

Therefore, the simplified expression is -1/4018.