I’m a photo lab technician. I work utter alone, for hours on end. I can go “out front” & speak with people, but not while working.
Some research jobs. At my last one I worked in a pitch black basement lab with only my infrared goggles/camera and SLDs to keep me company. The only times I saw somebody was during the biweekly meetings.
Transcriptionists often work alone. I have a friend who does medical transcription in her home. She hardly ever sees another human being except when she goes out to buy groceries.
Don’t know how real this is, but in Northern Exposure, there was a guy who worked in one of those fire-watch towers. Lived in a cabin up on stilts and spent his entire day looking for smoke. He was on medication because he could barely handle the stress.
Bomb disposal?
Test pilot?
Mime? 'cause, once you’re in that invisible box…
Software virus author? I can’t imagine there are too many companies out there pumping the stuff out…
I’m putting my vote towards “eccentric scientist”. I tend to favor eccentric chemists, at least they are exposed to volatile chemicals.
Take Henry Cavendish, he freakin’ discovered Hydrogen. And yet he was terrified of strangers and his servants. He communicated to his servants soley through notes and even built a separate entrance for them to avoid them. I believe he even constructed a secluded path from his house to his laboratory so no one would see him. Even his clothes were eccentric. His faded velvet coat and three-cornered cocked hat hadn’t been in style for a century.
However, make sure to be an “eccentric” scientist. “Mad” scientists tend to attract the company of the fleeing masses and heroes in tights. 
Habitual sperm donor?
I often work alone in retail, but I’ve got customers as ‘human’ contact. 
I’m on my own in work terms, but not alone completely.
I used to work as a lab tech in the weekend shift. There were other people in the factory, 3 if we had the day shift and 4 if it was night.
On a day where I saw a lot of people, we’d all be having one meal together and I’d get 4 or 5 visits from guys bringing samples.
Depending on what was Production doing, I might not see anybody for the whole shift, just call in to the foreman when I arrived.
Not exactly working alone, but it certainly let you blast away with whatever music you happened to like 
Has no-one mentioned truck drivers?
See post #6.
…
Damn…today is just not my day.
Okay I’ve got one. I’ve been through the entirethread and I haven’t seen it mentioned…
Night-time Security Guard. I’ve met a couple of these guys while working with my stepdad on building jobs. I don’t know why but they always wear black like it’s the unwritten code of the security guard.
I was a photo lab tech for years before I became a custom framer. I’m alone except when customers come in. Yes… I talk to myself. A lot. 
I deliver newspapers, which gives me a couple of hours of much-needed solitude every day. It’s great…sort of like getting paid to drive around and listen to your radio.
In the past I’ve often worked while camping out without seeing anyone else for several days at a time. Even when working as part of a group I’d spend most of my working day alone in the forest. Nowadays, though, I usually have a field assistant along.
I used to, and still do occasionally, work for the Web site of the newspaper. I’d go in at 4:30 p.m., and my coworkers would all leave by 6, and then it was just me until 1:30 in the morning.
And that’s how I racked up over 3,000 posts on the SDMB.
My Uncle Gordie has been a lighthouse keeper on Machais Seal Island (Canada’s only remaining staffed lighthouse). Many years prior to this, in the late 40s and 50s, he flew back and forth across the arctic keeping track of the ice. In those days there were also a few isolated ice stations (now all met stations are in comunities, such as Eureka on the top of Ellesmere, where my cousin works). Given the difficulties of re-supply, the individuals at a few of these stations were only relieved every six months. My uncle has a hilarous tale of one of these fellows who started talking on the radio about his girlfriend. Everyone figured that against all odds an inuit woman had come across him and tagged up with him.
When it came time to extract him, they learned the truth – his spouse was one of the chickens with which he had been supplied six months earlier. :eek:
Truck drivers can work alone, but you see a lot of married couples co-driving a truck as well. My sister, for example, drives a truck with her husband. With two people in the truck, you can keep rolling 24 hours a day. It’s easy enough to put a small fridge and a microwave in a big truck, so you only really have to stop for fuel, showers and bathroom breaks.
My part-time computer operators on the weekends work alone. They only see another person at shift change, or when one of the system administrators go in for some reason.