Windowed DISTINCT aggregates

You may have discovered that the use of DISTINCT is not supported in windowed functions. A query that uses a distinct aggregate in a windowed function,

SELECT COUNT(DISTINCT something) OVER (PARTITION BY other)
FROM somewhere;

will generate the following error message:

Msg 10759, Level 15, State 1, Line 1
Use of DISTINCT is not allowed with the OVER clause.

There are, however, a few relatively simple workarounds that are suprisingly efficient.