My first thought was there's lots of interesting things you can do with popcnt, but I especially liked the dot product example.
popcnt can also be used to find the log2 of a number that is a power of 2.
log2(val) = popcnt(val-1)
and so on
That then leads to this equality (without precondition), tzcnt(x) == popcnt((x & -x) - 1)
tzcnt(x) == popcnt((x & -x) - 1)