Let's evaluate the given expression step by step:

\[
\left(\frac{1}{2} - 1\right) \left(\frac{1}{3} - 1\right) \cdots \left(\frac{1}{9} - 1\right) \left(\frac{1}{10} - 1\right)
\]

First, simplify each term inside the parentheses:

\[
\frac{1}{2} - 1 = \frac{1 - 2}{2} = \frac{-1}{2} = -\frac{1}{2}
\]

\[
\frac{1}{3} - 1 = \frac{1 - 3}{3} = \frac{-2}{3} = -\frac{2}{3}
\]

\[
\frac{1}{4} - 1 = \frac{1 - 4}{4} = \frac{-3}{4} = -\frac{3}{4}
\]

\[
\frac{1}{5} - 1 = \frac{1 - 5}{5} = \frac{-4}{5} = -\frac{4}{5}
\]

\[
\frac{1}{6} - 1 = \frac{1 - 6}{6} = \frac{-5}{6} = -\frac{5}{6}
\]

\[
\frac{1}{7} - 1 = \frac{1 - 7}{7} = \frac{-6}{7} = -\frac{6}{7}
\]

\[
\frac{1}{8} - 1 = \frac{1 - 8}{8} = \frac{-7}{8} = -\frac{7}{8}
\]

\[
\frac{1}{9} - 1 = \frac{1 - 9}{9} = \frac{-8}{9} = -\frac{8}{9}
\]

\[
\frac{1}{10} - 1 = \frac{1 - 10}{10} = \frac{-9}{10} = -\frac{9}{10}
\]

Now, multiply all these simplified terms together:

\[
\left(-\frac{1}{2}\right) \left(-\frac{2}{3}\right) \left(-\frac{3}{4}\right) \left(-\frac{4}{5}\right) \left(-\frac{5}{6}\right) \left(-\frac{6}{7}\right) \left(-\frac{7}{8}\right) \left(-\frac{8}{9}\right) \left(-\frac{9}{10}\right)
\]

Notice that each term is negative, and there are 9 terms. The product of an odd number of negative numbers is negative. So, the overall product will be negative.

Next, multiply the fractions:

\[
\left(-\frac{1}{2}\right) \left(-\frac{2}{3}\right) \left(-\frac{3}{4}\right) \left(-\frac{4}{5}\right) \left(-\frac{5}{6}\right) \left(-\frac{6}{7}\right) \left(-\frac{7}{8}\right) \left(-\frac{8}{9}\right) \left(-\frac{9}{10}\right)
\]

The numerators and denominators will cancel out sequentially:

\[
-\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8 \cdot 9}{2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8 \cdot 9 \cdot 10}
\]

This simplifies to:

\[
-\frac{1}{10}
\]

Therefore, the value of the given expression is:

\[
-\frac{1}{10}
\]