Brainf*ck, 81 characters (no whitespace)
,[>>>[->>+++++[-<+++++>]<+<]>[-<+>]<<++++++++[<++++++++>-]<[<->-]<[>>>+<<<-],]>>>
Explanation
,[ // get character input into p[0], enter loop if it isn't null (0)
>>>[->>+++++[-<+++++>]<+<] // take what's in p[3] and multiply by 26, storing it in p[4]
>[-<+>] // copy p[4] back to p[3]
<<++++++++[<++++++++>-]< // store 64 in p[1]
[<->-]< // subtract p[1], which is 64, from the input char to get it's alphabetical index
[>>>+<<<-] // add p[0] to p[3]
,] // get another character and repeat
>>> // move to p[3], where our final result is stored
So you'll notice I didn't actually convert the numerical value to an ascii string for printing. That would likely ruin the fun. But I did the favor of moving the pointer to the cell with the result, so at least it's useful to the machine.
Hey, what do you know, I beat C#!