Apparently Russian peasants used an interesting alternate algorithm for multiplication.
The algorithm is quite simple.
1. Write the two numbers that you are multiplying side by side.
2. Create a column under the number on the right. Each entry should be half of the entry above it, ignoring any fractional amounts (example: if the number 5 is the right column, the number below it should be 2), stopping when the number 1 appears.
3. Create a column under the number on the left. Each entry should be twice the entry above it. Stop when the left column has the same number of entries as the right column.
4. Cross out any number in the left column whose corresponding number in the right column is even.
5. Add the numbers in the left column which are not crossed out.
The number you find in step 5 is the product of the two numbers you started with!
Example:
32 25
64 12
128 6
256 3
512 1
-------
800
So 32 x 25 = 800.
As liveforever pointed out to me, this method is of course commutative.