MMM has a small window where it can work.
In PVT, 3x rax play vs toss on close position can be very threatening (especially if you bring scvs with your push), but once toss gets collossi, sentries and HTs, gg.
TvT, if you only use MMM (no tanks) and be very active with drops, it can work (especially if your opponent goes typical marine,tank, viking) 'cause you're abusing his immobility.
ZvT, doesn't work 'cause ling/bling (especially if he has infestors) completely shuts down bio play.
Yeah, there is a small window for it work. However, when the protoss starts getting Collosi, you can easily masspump vikings and smash the collosi. The beauty of MMM is that its gas lite, so you can afford to get gas heavy units like Ravens. Raven+viking= lots of dead collosi. HT is very much more troublesome, but you can get ghosts to counter them.
TvT, depends on spawn location. Close = tank wars, so you will need tank support, preferably with Viking + Banshee. Plenty of things which will work here, as long as you are careful. Maurauder heavy builds seem to work too, as long as you get them before they have a critical number of tanks.
ZvT, welll you have ling bling, but if you mix a few hellions and with proper micro (watch MarineKing.Prime), its easy to pull it off, just needs a bit more apm. True, if the Zerg econ is bigger than yours, you will have problems, but on equal economy, its quite easy to micro your MMM and completely negate blings. Position wise, this is the hardest I think.
Very often, I get 2 Engineering bay early to get mass upgrades. MMM with +3 attack and def is nothing to sneeze at. And they need a lot of "bolt ons" to work perfectly. Just pure MMM is quite hard to pull off.
Side note: Tanks get weaker as the map size gets bigger and more non-linear. Split your MMM ball into 2 or 3 pieces, and simultaneously drop in different bases, and MAKE SURE TO KEEP THE OPPONENT'S TANKS IN DEFENSIVE POSITION INSTEAD OF ATTACKING. That caps is the most important part in any MMM success. Pressure + mapcontrol. Punish them if they move out.