Can a single bullet from a handgun kill three people in the way Deadpool did?

TL;DR: It is possible, but not very easy to pull off.

Real life examples:

One bullet, two deer killed:

A few years ago, a 10 year old boy on his first hunting trip killed two deer with one round.

One bullet, two men killed:

In 2009, a British sniper in Afghanistan killed two suspected insurgents who were fleeing on a motorcycle; the bullet passed through the heads of both men.

The Barrett .50 BMG anti-matériel rifle fires an enormous bullet - far too big for any handgun - but we're talking about a round traveling a mile, passing through a 10" thick wall, passing through one person, then passing through another. The human skull is only 1/4 inch thick, so passing in and out of 3 skulls in succession would mean traveling through 1.5 inches of bone. At close range, a handgun of average firepower could do this quite easily.

One bullet, seven wounds, one man killed, one wounded:

One of the bullets that hit John F. Kennedy entered the back of his neck, exited from the front of his throat, went into Governor Connally's back, out his chest, then into his forearm and out through his wrist, finally lodging just below the skin of his thigh.

Along the way, this bullet damaged one of Kennedy's vertebrae, shattered one of Connally's ribs, and broke a bone in Connally's wrist. Thus we see that bullets have considerable momentum, and can often punch through multiple surfaces/victims, doing extensive damage on the way, before coming to rest.

One bullet, five wounds, one man killed:

An autopsy on a boy in India showed that he had died in an accidental shooting, and the bullet had caused five wounds (link: warning - extremely graphic): it entered below his knee, exited above it, entered his hand, exited his wrist, and finally, entered his chest.

One bullet, 17 wounds, 9 men hit:

It is said that an imperialist adventurer once tied 12 Unangan men together in Alaska and fired a single round from his rifle at them. The round passed through eight of the men, lodging in the ninth.

Deadpool:

Deadpool isn't firing an anti-matériel rifle, nor is he firing the .50 BMG, but he has the next best thing: his primary weapons are a pair of IWI Desert Eagle Mark XIX .50 handguns. These are among the most powerful handguns ever made, and they have more than enough muscle to do the job.

Give him an infinite supply of ammunition and perfectly lined up skulls and he can score 3-for-1 shots all day long. The only tricky part would be a real life scenario in which the targets are running around doing everything in their power to avoid being shot.

As Voo generously said in a comment:

I used this calculator to get the kinetic energy of the bullet used in the Kennedy shooting (162grains, 1700fps) - 1410 joules). The desert eagle has a maximum muzzle velocity of 150fps and there's 325 grain heavy ammunition for it. So from a close enough distance at least the energy would be more than enough

And Dan Neely added:

The 9mm (362 joules) and .45 ACP (432) are the mainstay defensive handgun rounds in the US. The DE .50 is several times more powerful and is one of the very few handgun rounds powerful enough to match a (low end) rifle bullet's performance. The reason why most handguns are much less powerful is to keep recoil manageable. Despite being absolutely huge for a handgun (mass reduces the felt effect of recoil), the DE .50 has a recoil that's beyond the ability of most people to manage and painful even then.

Yes, but no.

It's feasible. But not likely. Consider it only shattered two skulls and deflected off the third. In fact, this bit seems to mirror a Mythbusters segment:

A bullet from a .50 caliber Desert Eagle pistol cannot penetrate 25 watermelons.

Tory and Kari set up a line of melons, but Kari's shot only penetrated the first three. They noted the parallels between this test and the use of a .50 caliber sniper rifle during "Bulletproof Water" (2005), in which the slug could not reach Adam through only a few feet of water.

They use a .50 AE caliber bullet in a Desert Eagle Mark XIX, exactly like Deadpool uses, shot from under 10 feet, just like Deadpool does, destroyed two watermelons, and barely penetrated the third, just like Deadpool did.

Full video at Discovery.com.

In the high speed video, you can actually see the bullet ricochet off the 3rd watermelon.

And they did it in a controlled environment with no movement of the heads or the gun, not on the fly like Deadpool did. In a perfect situation, the same bullet from the same gun reacts in pretty much the same way.

It's almost as if they stole the scene from the Mythbusters along with the countless references in the movie.

In real life, bullets of any caliber are really really unpredictable once they hit anything. The entire field of Terminal Ballistics attempts to study this, but one bullet can go straight through an object while another could deflect, or ricochet. Sometimes people are hit, the bullet going straight through, other times it will bounce around like a wild super bouncy ball. Another time it fragments making it worse. That the bullet goes straight through two skulls into a third is statistically hard to quantify.

Terminal Ballistics as Viewed in a Morgue –gunthorp

But then, I've seen most everything. I've seen a guy killed by a .416 Rigby, as well as a suicide to the head with a .44 Mag that didn't penetrate the skull on the other side.

The long and short of it is that you just don't know how ANY bullet will react to tissue and bone until you open them up and take a look. I've seen hardball fragment and hollowpoints act just like hardball. That said, shoot what you're comfortable with and place your shots well whatever caliber you use.

The heaviest grain .44 Mag has a very slight advantage over a .50 AE in its ballistic performance judging by energy (joules), and makes for an apt comparison to the caliber of Deadpool's weapon.

Combine that with the above mortician's experience, and the answer is you are by no means assured that it will even pass through the first person's skull, let alone three.

I've yet to have the stomach to further delve into skull-penetrating capabilities of specific cartridges, but there is no doubt in my mind that under the right circumstances, it is entirely possible.

In the movie the three men were caught by surprise and in a perfect lineup. At less than 10 feet, with that weapon, I would say it is very possible.

Having said that, Deadpool only killed 2 men with that shot. The third man was hit, but the bullet didn't penetrate his skull.