Assuming that you want computing in the numerical sense, and don't require electronics, then you can do many things with clockwork. Wikipedia gives a better summary than I can: https://en.wikipedia.org/wiki/Mechanical_calculator#Mechanical_calculators_reach_their_zenith
For the general-purpose "computer" of today, you're likely to run into the same problems as Turing, Lovelace, and Babbage - too many parts.