Well, honestly, I don't think you could increase your APM just by watching videos of progamers with blistering APM. 

Like what Marksman said, you play lots of meaningful games where you strive to do something faster and more efficiently.

Of the videos I posted, I think the slowest one is IdrA. He plays fast but very, very efficient, not mindless spamming between 2 buttons.

Instead of just focusing on APM, try to polish your mechanics.  If you play Zerg, that means not missing your injects and spreading creep.  If you play Terran, you keep up with your Mules, split your forces.  If you play Protoss, use your Chrono energy.

I played a ZvP Elite AI last night to take note of how I play, so that I could add to this thread.

Focus one 1 or 2 openings (I used to call it "build" in SCBW, but in SC2, I would rather call it "openings" as the game clock allowed me more flexibility).  I play zerg, so I did this by learning a pool-first opening and a hatch-first opening.  (For Terran and Protoss, this may mean learning a 1-base opening, or 2-base opening.)

I timed everything.  I always go 9 overlord, and I make sure that I made that overlord before between 00:51 and 00:54 game time.  If I open pool-first, I take one drone and move it towards where I want to place my pool when I see that I have 175 minerals (I also make sure that I don't pick the drone that's on the close mineral patches).  Then on the split second I see 200 minerals, I put down my pool.

And when I make my 2nd hatchery, I take a drone at 200 minerals and move it towards the natural.  It arrives at the natural base when I have 290 or 295, then I make my hatchery the split second I see 300.  Then I click on the 2nd hatchery, go shift-4, rally to a close mineral patch, press 4 (to choose both my hatcheries) then right-click near the opening of the natural, then go "S-D" to make a drone.  From the moment I make my hatchery, I think I did all that in less than 2 seconds.

I normally have my first overlord at Ctrl group 1, so I go "1-1" to check where it is and what it's seeing.  Then I go "4-4" to look at my base to continue my opening.  I have my hatchery selection button (originally the "~" button) also bound to my mouse's "back" thumb button, so I could scroll through my hatcheries quickly.

When I make a refinery, I make sure to put 3 drones in it as soon as it finishes.  Then when I get my first 100 gas, I make sure to make use of it by going ling speed (or lair).  If I went ling speed first, I use the next 100 gas to go lair.  Or if on a ZvZ, I use the next 50 gas to make a baneling nest. 

I also notice that I hit "4-S" and "5-5" throughout the game (I have all my queens on "5").  As mentioned above, I have all my hatcheries on "4" and hitting "4-S" allows me to select all my available larvae.  I also notice that after a "4-S", I usually look at my mineral and gas bank. This tells me how much I could spend for units and how many of each unit I could build.  I go "5-5" to center on the nearest Queen.  I don't necessarily look at the Queen, but I look at the hatchery, to check if I need to inject, and how long I have before I need to do the inject.

So, yeh, basically, everything I do has an underlying purpose for it.  I'm not saying that what I do is correct and you should follow it, but my point is, do what feels most comfortable to you. Another underlying point is, noticing and improving on the little things ultimately make you faster due repetition.  And in this game, doing something faster and more efficiently, makes you better.