I'll be interested to see if someone can come up with a better solution, but this is what I drew up after reading the question...presuming the value to be examined is in cell A1:

=SUM(IF((LEN(A1)-LEN(SUBSTITUTE(A1,{"A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z","1","2","3","4","5","6","7","8","9","0"},""))),1,0))

The advantage of the above is you can be specific about characters to count....for example, the above ignores spaces.

I'm sure there are other ways to do this, but maybe this will work just fine.