It’s hard to know how often this perspective is really used because it’s somewhat overlooked. I have had the five perspective classifications in my head for so long that I can’t remember who first taught them to me. What I do remember is some teacher at some point telling me that this point of view (which I remember being referred to as both Third Person Objective and Third Person Limited) was even less popular than second person. If the sparse Wikipedia mention is any indication (it doesn’t even have its own page!), third person objective (TPO from here on because I am lazy) has gone from unpopular to nearly discarded.

This style, like second person, has a lot of intrinsic restrictions. The story you get in TPO is the same kind of story you would get from a private investigator who has been following your characters. He can describe what they did and said, but can give no true insight into their thoughts and motivations.

The basics of TPO are as follows:
– I and we are used only in dialogue
– All characters are referred to by name or by the distant pronouns he/she/they
– You cannot delve into any character’s thoughts, not even your protagonist’s

For example:

He sat in her seat at the kitchen table, placing his hands where hers had rested so many times.

“I still take care of your roses,” he said to the air.

The silence that reigned then was broken only by the ticking of the old clock hanging on the wall. He sat there for another minute and sighed.

“I should accept the fact that if you haven’t come back by now, you’re not going to.” He stood and gently pushed the chair back into place. “But I still feel guilty that no one will be here to take care of the roses once I leave.”

All the information you get from the segment above comes from her observable actions and the words he speaks aloud. Sticking to that, keeping yourself from accidentally filling in the blanks, if the hardest part of writing in TPO. An upside, however, is that you can peer through anyone’s window, peek into their lives (a peek that all three third person perspectives include).

Excepting this, TPO is the most distant point of view, watching but in no way involved. Think back to my investigator example–in a way, reading a book in TPO is more than a little like reading a PI’s report. Not that it’s never used successfully. In fact, one of my favorite short stories is in this narrative style: Hills Like White Elephants by Ernest Hemingway, which you can read by clicking the title. However, unless you have a genius narrative idea like Hemingway’s, you’re probably better served by one of the other points of view.

See Also:
POV Overview
First Person
Second Person
Third Person Limited Omniscient
Third Person Omniscient

EDITED TO ADD (12/17/2016):

In my two Assassins novels, I make use of this point of view often. For those books, Discord and Nemesis, the TPO perspective allows me to give readers a look at what’s happening away from the narrator. I can give away secrets the narrator doesn’t know, or at least leave clues, and it adds suspense to the pacing of the books. Below is an example from Nemesis, and it is the very first section of the book:

The vicious squall battered the Sea of Japan, roiling the waves and sending high winds screaming across the water. Those waves crashed against the shores of the small, isolated island sitting between Japan and the Korean Peninsula. Wind battered trees and displaced rocks on the island’s tall mountains.

Inside the Lyohwa Labs research facility on the northwestern edge of Etobih-lin, none of that could be heard. Especially not on sublevel two.

Lab six was a large, windowless room with a door that couldn’t be opened from the inside. Cameras in the corners were positioned to monitor everything, with no blind spots, but at this early hour of the morning, there didn’t seem to be much to watch. Only one woman—wearing a white, full-body, level A hazmat suit—was at work.

Hands braced on a backlit glass table, she stared through her faceplate at the rack of glass vials in front of her, furrows across her forehead. The vials seemed to glow with the light from the table, and the intensely green liquid was vibrant in the otherwise stark white and stainless steel room. Though her gaze jumped between the vial and the tools laid out in front of her, she ignored the alerts popping up on the wall-mounted screen to her left and the beeps of the various machines, all of them labeled LyoLabs.

“They’ll kill you if this works.” The words were quiet, but the distortion of her breathing apparatus gave them an ominous rasp. “Whatever. At least you won’t be here anymore, right?”

However cavalier the words seemed, her hands shook when she straightened and tried to lift a vial out of the rack with a pair of tongs. She took a deep breath, the sound made mechanical by her respirator. Her hands steadied. After lifting it clear of the rack, she turned and placed it in another on the epoxy resin workspace behind her.

Slowly, carefully, she extracted a small amount of the green liquid with a pipette and placed three drops into the brown mixture simmering in a beaker over a lit Bunsen burner. The color shifted as the bright drops swirled and dissolved into the bubbling liquid. From a vacuum-sealed jar on the table, she measured out 0.03 milligrams of an extremely fine powder. When she added it to the beaker, lines of dark blue spread through the mixture like ink, but when she stirred it with a thin glass rod, the solution cleared.

“Almost there.”

Another alert buzzed through the computer’s speakers. The tone was lower—a grating sound meant to draw attention—but she didn’t spare the screen more than a cursory glance.

The door behind her opened; the hiss of the airtight seal releasing would have made that obvious even if the door’s handle hadn’t clicked as it lowered and announced company.

A leanly muscled, olive-skinned guy wearing a LyoLabs security uniform walked into the room, a Colt handgun in his hand. He kept it pointed at the floor.

“I don’t care how impatient you are,” she said without turning around. “There is no possible way for me to make these machines work any faster. Either shoot me, or let me get back to my work.”

“Adila?”

“Who else?” she muttered. “It’s not like you assholes let me have assistants anymore.”

He stopped at the wall display that had been flashing a red alert box. When he saw what was written there in bold black-and-white Korean letters, he cursed. When he crossed the room, his footsteps were heavy and quick. “Adila, we have to go. Now.”

“Go. Stay. Come. Work. I’m not a goddamn dog!” She slammed her hand down. The stirring rod clenched in her fist shattered when it hit the countertop. Releasing the broken pieces, she turned. “If you want me to figure this out, leave me alone and let me— Who are you?”

Though the gun-wielding newcomer was dressed as a guard, he looked like he might be twenty at the oldest. He seemed too young to be working there, but his dark eyes searched the room with purpose, and he held his Colt like someone with decades of experience shooting it.

“I’m your ticket out of here if you follow me,” he said. “But the offer won’t be worth anything in about four and a half minutes.”

Adila hesitated only a moment. In a burst of motion, she grabbed a flash drive and jammed it into one of the computers, activating a command to back up the data.

“Time is running out,” the guy warned. “Is that info worth our lives?”

“It’s worth a hell of a lot more than that.” Adila dumped the clear liquid from the bubbling beaker into the sink, then filled the beaker with a solution from a large bottle next to the sink, and poured the rest of the bottle’s contents and all of the green-filled vials down the drain. When the computer flashed Backup Complete, she ejected the flash drive and pressed it into her rescuer’s hand.

After executing a command to format the computer and wipe the drive clean, Adila followed the stranger out of the lab, slowly stripping the hazmat suit as she walked, dropping the pieces behind her.

As the suit fell away, the body underneath it became visible—and the scars that body wore. Old, healed burns from pinky finger to elbow up the side of her left arm. A misshapen bump that might have been a badly treated break. Thin lines were almost hidden in the natural creases of her neck, but they were too pale against her naturally tan skin to disappear completely.

“Annyeong, fuckers,” she said as the door shut behind them.