In order to do this we need a baseline.
baseline macro minimum:
A worker is produced every 17 seconds(15 for Z)
a supply building/unit takes 25 seconds for P/Z and 30 for T to build, and is needed every 136(120 for Z)seconds for workers alone.
therefore a potential baseline APM for the bare minimum of macro is:
P: 9.8+9.8 APM per Nexus baseline APM
T: 9.9+9.9 APM per command baseline APM
Z: 13.9+9.3 APM per hatch baseline APM
solely required to constantly produce workers from one base.
From this we can infer that Zerg requires the most baseline APM in most situations.
NOTE: this is ignoring macro mechanics at the moment we will get to those next
P(Chronoboost): 5.5 APM +4.1 APM per Nexus
T(Drop Mule): 2.0 APM +1.3 APM per Orbital
Z(Inject Larva): 4.1 APM + 4.1 APM per Queen/hatch
if we add the macro mechanics to the baseline required APM we get:
P:15.3 APM + 13.9 APM per Base
T: 11.9 APM + 11.2 APM per Base
Z: 18 APM + 13.4 APM per Base
Now a breakdown of constant unit production per production facility:
Protoss (note that chronoboosting any of facilities will add to the APM requirements generally by about 1.3+0.6 per additional chronoboosted warp gate, and more for robo units and stargate units)
Zealot: 8.6 APM + 2.1 APM per additional warp gate
Stalker: 7.5 APM + 1.9 APM per additional warp gate
Sentry: 8.9 APM +2.2 APM per additional warp gate
Dark Templar: 5.3 APM + 1.3 APM per additional warp gate
High Templar: 5.3 APM + 1.3 APM per additional warp gate
Archon: 8.2 APM + 3.9 APM per additional 2 warpgates
Immortal: 2.2 APM + 1.2 APM per additional Robotics facility
Observer: 3.0 APM + 1.5 APM per additional Robotics facility
Collosus: 1.6 APM + .8 APM per additional Robotics facility
Warp Prism: 2.4 APM + 1.2 APM per additional Robotics facility
Pheonix: 3.4 APM + 1.6 APM Per additional Stargate
Void Ray: 2.0 APM + 1.0 APM per additional Stargate
Carrier:1.0 APM + .5 APM per additional Stargate
Marine: 4.8 APM + 2.4 APM per Reactor/ additional Barracks
Marauder: 4.0 APM + 2.0 APM per Additional Barracks
Ghost: 3 APM + 1.5 APM per Additional Barracks
Reaper: 2.7 APM + 1.3 APM per Additional Barracks
Siege Tank: 2.7 APM + 1.3 APM per additional Factory
Hellion: 4.0 APM + 2.0 APM per Reactor/additional Factory
Thor: 2.0 APM + 1.0 APM per additional Factory
Viking: 2.9 APM + 1.4 APM Per Reactor/additional starport
Medivac: 2.9 APM + 1.4 APM per reactor/Additional starport
Raven: 2.0 APM + 1.0 APM per additional starport
Banshee:2.0 APM + 1.0 APM per additional starport
Battlecruiser: 1.3 APM + 0.7 APM per additional starport
Zerg (note that zerg unit constant production is based on larva creation speed, and as such APM requirements increase with inject larva and decreases when droning, also note the APM requirement only SEEMS higher than other races, the increase in APM is per additional hatchery, zergs will have as many as 7 hatcheries in some games and as few as 2 in others unlike other races which can have dozens of production facilities)
Zergling: 12 APM + 4 APM per additional Hatchery
Roach: 12 APM + 4 APM per additional Hatchery
Baneling: 16 APM + 8 APM per additional hatchery
Hydralisk:12 APM + 4 APM per additional Hatchery
Overseer 16 APM + 8 APM per additional Hatchery
Mutalisk 12 APM + 4 APM per additional Hatchery
Corruptor 12 APM + 4 APM per additional Hatchery
Infestor 12 APM + 4 APM per additional Hatchery
Ultralisk: 12 APM + 4 APM per additional Hatchery
Brood Lord: 16 APM + 8 APM per additional Hatchery
Now knowing our Macro based APM requirements we can look at typical APM requirements for producing the armies that we are used to seeing in builds.
For instance, a two base Protoss with 7 gate 1 robo going for stalker colossus has to spend 51.6 APM solely producing his units, + APM for pylons
A typical ZvT build has a three base Zerg producing at with 68.8 APM + APM for overlords.
A common 1/1/1 build for Terran will have them using 24.7 APM + APM for supply depots off one base in order to produce the army required.
Now these are not comparable numbers, only examples, no one should take out of this that Zerg requires the most APM because a three base Zerg needs more APM than a one base Terran with only 3 production facilities.
There are a few things we can learn from these numbers, knowing they are low enough that we are all capable of the speed, if not the accuracy required for macro of most strategies, but can marvel at professionals skill at doing all of this AND micro, which can include perfect blink stalker micro (which is 18 APM per stalker) is truly amazing. Also good to know is that all of these APMs are in Starcraft 2 time, so it's even faster for real time.