Russian Peasant Multiplication
I've been using a less strict version of this method to multiply in my head since I was a kid.  Nice to know there's a name for it.You can also take advantage of multiples of 5 and 10.  For example:   115 x 37 = (100 + 10 + 5) x 37
   = 3700 + 370 + 370/2
   = 3700 + 370 + 300/2 + 70/2
   = 3700 + 370 + 150 + 35
   = 4255