personaly, I wish to God that my job didnt involve meeting the public. Im in retail, and it seems that a very high percentage of our clients are mad or weird, or both. I have voiced the theory that the bright lights in our window attract them; a veritable beacon for nutters.
I deliver newspapers, and beckwall is right–it’s nice and quiet. Not sure you could make a living at it, though, if you have a family. I make about $1300/month, and I’m pretty much tapped out as far as how many papers I can deliver. If you run late, though, you gotta talk to all the old folks waiting on their steps for their papers.
I also proof read; there’s a nice quiet job for you. Boring as hell, somewhat stressful, but quiet. Submit 100 pages/day and you never have to talk to anyone unless you have a question. The money, again, isn’t great, but it’s a decent part time job.
Emofkuniv How well I can relate… I opened a retail business myself… I think 90% of the oddball fruitcakes in town choose to frequent my store…
My job is pretty sweet non-interaction-wise. I’m a merchendiser for Hallmark so many times I’m in and out of the store without saying “boo” to anybody. I have a little hand scanner and scan in when I arrive, go to the back room to see if any orders came in, tidy my area and put out any product, scan in orders, scan out of the store, then transmit everything over the phone when I get home. I have to talk to the store receivers on occasion because the seasonal returns get shipped out every couple months or so, but hell, even then it’s just the one guy and you can usually just say “here” and he goes “thanks.” If customers come up and talk to you, 99% of the time they’re looking for something elsewhere in the store and you can just say “sorry, I don’t work for the store, just Hallmark.” The downside of this job is you’re not going to get rich and retire off it. I make $9 an hour and work maybe 10 hours a week (excepting major holiday weeks, obviously.) It’s a great job though, because I can pretty much pick my own hours as long as everything gets done.
I have to confess, that sheepherder job sounds tailor made for me though!
If you want the most isolating job in the world, become a ‘house-cleaner’. I did this for quite a few years to supplement my meagre Sole-Parent Allowance (cash-in-hand thankyouverymuch), and working for professional people and DINKS, rarely ever saw the people who actually lived in the houses that I cleaned. I’d let myself in, vacuum and dust and whatever, and let myself out with absolutely nil human interaction (although there were often dogs to keep me company!!)
If you like living in your own head, take on house-cleaning. 
Professional assassin comes to mind.
Fur trapper.
Windmill farm maintenance man.
Wiretapper/electronic surveillance operator.
Mad bomber, aka Ted Kuczinski.
My brother-in-law works as an ‘unloader’ for Fed-Ex. It’s a graveyard shift, move-boxes-around sort of deal. He’s very, very, very shy and he loves it.
One summer I worked swing shift as a lab tech for a cherry packing plant. I loved it. I had the entire lab/office area to myself. There were a few hundred people out running the plant, and I’d go out hourly to take swabs/samples, but rarely had to talk to anyone. My supervisor would be there for an hour when I first came in, then I’d be on my own for the next 6-10 hours. Sometimes I’d have to contact a shift manager by radio if the temps or brine compositions weren’t right, but 90% was no people.
Oh yeah. My uncle was a night watchman at some sort of high-tech firm. He’s written a few novels while sitting around at night “working.”
With that many sheep around, who needs a hooker?
Hmmmm…
The perfect ones! 
My job is almost like that, although it doesn’t sound like it would be. I’m a videographer for a wedding chapel. I work in a small video booth next to the inner chapel. I run the cameras, sound, music, etc., from there. The wedding party and guests don’t see me, and I never have to interact with anyone, besides giving the finished video to the chapel staff to give to the happy couple. I think it’s almost the perfect job: I go in, do my job, get to play with tons of expensive equipment, don’t have to interact with anyone, and go home. Plus, I work an average of 10-20 hours a week, so I have lots of time off.
Tesa
Huh. I had a few “invisible” clients, but also quite a few elderly people who thought that listening to them ramble on about their grandkids/TV shows/pets/medical problems was part of my job description. There was also a woman who would leave her kids with me while she ran errands (I charged $2 extra; they were good kids; she didn’t mind paying), a man recovering from heart surgery whose wife asked me to “check” on him periodically, and a woman with OCD who oversaw everything, and I mean everything, that I did. Why she didn’t just do it herself, for free, I don’t know. And those were my freelance jobs. When I was with an agency, we always went out in twos or threes, because we were doing the really big mansions that were not a one-person job.
I was an on call technician for a very secure . . . government thingie.
Not only did the thingie work just fine every single day that I was there, so that I had not a single damned thing to do, the entire seven months, but there were three locked doors between me and the nearest human being, and he didn’t have the keys.
I showed up. I grunted at three different guys who grunted back, as I walked through the first of those three locked doors. Then I made my phone call, to let the folks who were supposed to call me if the thingie broke know that I was there. Then I called the guy who was at the other place where they could call and told him he could go home. Eight hours later, the phone rang, and the guy who came in in for the next shift told me I could leave.
There was no one I could have interacted with if I had wanted to. Three times in seven months my supervisor came by. One of those times, he didn’t make it passed the second door. The other two times, he asked me if I had been asleep. I said no. He didn’t believe me, but he didn’t care. The phone was loud enough to wake me anyway. He left.
I hated that job.
Tris
Oooh! Now that sounds like the perfect job! No co-workers to pester you. No clients/customers/civilians to piss you off. And hardly any supervision whatsoever. You could even catch up on your sleep if you wanted and no one cared.
However, I get the feeling that the true downside to that job was that the government thingie had the potential to either explode or cause an international incident, or both. 
But, hey, every job has its drawback.
Tesa