We know that, recently, personal computers make around $10^9$ calculations per second, and I'm just curious about how many calculations was able to compute the machine invented by Turing for breaking the enigma code.
This is only a very rough, back of the envelope answer because there were several versions of the enigma and the Bombe, but according to the Wikipedia article on the British Bombe, one version of the Bombe could
run through all 17,576 possible positions for one rotor order was about 20 minutes
Since $17576 = 26^3$, it's referring to the three-rotor version of the enigma. That comes out to about 15 operations a second.
Rob is correct that computing speed progressed extremely rapidly at this point too, so my answer represents a basic answer about one single machine, and obviously there were many others of varying capability as time went on.