Shared interests/hobbies, but there has been a work-related component a couple of times: had our jobs/interests not brought us together we might not have met.
In the case of my wife, we did have some mutual friends, but our relationship started after her job put her in frequent contact with me.
In the case of another relationship, it was her interest in things that were connected to my job.
Earlier relationships began through hobby-related groups, amateur theater in particular.
I tried online dating for a while (with mixed success), but I met my wife when my former classmate set me up with his co-worker’s former classmate.
My former classmate invited me out to lunch, and when I got there he told me: “I don’t really want to have lunch with you. Would you like to meet that girl over there? If you don’t, I’ll just blow her off.” It was an ambush, I tell you!
One I met at the food court in a mall.
One I met while working a part time job.
One I met in the parking lot of an apartment I was moving into to get away from the one I met at the food court in a mall.
One I met at work.
One I met through my brother.
One I met at a bar. He’s the one I still have.
I was shy to the point of being terrified of guys when I was in high school, so no boyfriends there. After I joined the Navy, I wasn’t shy any longer, and being in a very definite minority (a gazillion men and very few women) in training situations, I was always being asked out by classmates and such. Since it was, technically, my job, I picked work to cover those situations.
I picked “Other” for my husband - he was my sailing instructor. We were both in the Navy, but we met at the base marina outside of a work situation.
The idea of going out on a date with a perfect stranger is absolutely terrifying to me. All of these guys were pre-screened through friends first, like elaborate friends of friends (or friends sometimes). Mad props to those of you who met people online. I know I couldn’t do it, which makes my dating pool extremely tiny.
In high school, one of my BFF’s was engaged to marry a young man. She asked me if I would like to be pen pals with his brother.
BFF is my SIL now, and the pen pal and I celebrate our 39th anniversary in June.
~VOW
I’ve had four long-term relationships in my life (though I never had anything approaching a long-term relationship until after I graduated from high school):
I met one in my Dungeons & Dragons gaming group
I met one in my college dorm (co-ed dorm, she lived on the floor below mine; I put her in as “Other” for the poll)
I met two as “friends of friends” (though, in both cases, the “original” friends were people with whom I played D&D), and I married one of those two. 
Yeah, I had meaningful relationships with people I met in HS, and married someone I met in college. I’ve had two online relationships, one of which ended with her untimely death, and the other is ongoing. In neither of those cases would I have called it “Online Dating”, though - we met on sites that were social or political chat places.
Wife (and occasional SD poster) Dunkelheit thought I was an asshole when she first “met” me online.
Huh. I’ve been dating for a long time, so for differing values of “significant” almost all of the above.
My most significant relationships of the past ten years or so? Three in bars, one on the subway, one online (but not a dating site), and one friend-of-a-friend. The one that might yet turn out to be the love of my life I met in a bar.
Four primary significant others:
Ex-wife: coworker on a different but overlapping shift at the same store. I’d had my eye on her for a while, but assumed she was taken. We went outside for a break, and she simply asked me why I hadn’t asked her out yet. I discovered after we were married that she had indeed been in a relationship at the time; he hassled me for a number of years, even after she and I divorced.
Ex-fiancee #1: at a dance club. I prefer to dance by myself, and she felt out-of-place being in a “meat market,” and we ended up talking, then dating for a few years. She’s the most sane woman I’ve ever dated, which is odd since everyone says it’s a bad idea to hook up in a club.
Ex-fiancee #2: at school, met her while dating the above woman. I was mentoring a logic course which required me to sit in on classes, and she sat next to me. I felt like she was hitting on me, and was very uncomfortable when she invited me over to her house for a party; ex-fiancee #1 didn’t like the idea either, and I didn’t go, nor stay in contact once the class had ended. Five years later, I was mentoring a different logic course, and the woman came to one of my mentoring sessions. Helped her the one time, and didn’t see her again until she contacted me out of the blue on Facebook, where she began pursuing me (despite living with her fiance) for the next six months. They broke up, I said “what the hell, might as well say yes now,” and I ended up in crazy-land for the next couple of years.
Ex-girlfriend: at work. Cute girl who caught my eye, but when I found out her age (legally an adult… by a couple of months, and literally half my age), realized there was no point in even trying. A couple of months in, she began to pursue me, and within a week we were an item. She had commitments to the military which would take her away in a few months, so it was never a serious thing, but it was a nice no-pressure, fun relationship that served as a palate-cleanser for the bad taste that relationship #3 had left.
I came home one evening and there was a girl sitting in a car. There was a huge cloud of blue smoke around the car, and the girl was crying. I knocked on the window and asked her if I could help. She told me that she had wanted to take good care of her car, and new that it needed to periodically have new oil. She had called her father and asked how much oil to put in, and he told her “Four quarts, five if you put in a filter” Just to be on the safe side, she had put in five quarts. She had not realized that she needed to drain out the old oil. She was sure she had ruined her car.
I got some tools and drained the oil. We went to the parts store and got a filter and more oil, and back to finish the oil change. We test drove the car, and stopped for Mexican food.
This was May 19, 1972. I made her pancakes for breakfast this morning…
In the “back room” of a gay porn theater. He was in the middle of a small group (he always got that kind of attention). Being very tall, he was able to look above the others, and make undeniable eye contact with me. Long story short . . . we went back to my place, and didn’t leave all weekend. There was no doubt that we had each found our “Mr. Right.”
More irritant than asshole, darling. 
But at least you could be reasoned with.
Oh yeah, and high school, work, public transportation, college, online and friends of friends.
In that order, actually.
I’m sure her family has stopped looking for her by now.
High school, college (not college classes, just normal college mingling), grad school, friends of friends, friends of family, personal ads (this was back in the pre-Internet era, since I’ve been off the market since 1988), and one relationship with a woman I met when we were volunteers together on a crisis hotline.
Met her in 2nd grade at a parochial school at age 7.
Didn’t date her until I was 19. Was talking to my best friend’s sister who was in the same Psych class as her; she commented on how smart and beautiful she was, so I decided to cold call her after 4 years from the last time I saw her in sophomore year in high school.
Became her husband at 23.
Been married to her for 26 years and counting.
We met at work in 1997, were coworkers for 2+yrs before we started dating, dated for about 3yrs, then got married in 2002.
Three long term relationships for me. HS boyfriend was in my class. College boyfriend worked with the husband of my boss.
Husband and I were technically coworkers, but we didn’t meet face to face for two years. At the time, we were both working for a large midwestern bank. I was in Kansas City, he was in St. Louis. We were assigned a project to design and support a small side computer program that created mortgage escrow statements. I was the programmer, he was in regulatory compliance. During the project we had a good working relationship, but never actually met - everything was done by phone and e-mail. Right after the project, his marriage collapsed, and he took the opportunity to transfer to Memphis. I sent him an Elvis mug as a going away gift. We stayed in touch and 6 months later, found ourselves invited to the same wedding in Memphis for two other coworkers. He asked me to be his date and offered to meet me at the airport. We finally met face to face that weekend. That was 17 years ago and we have been together ever since.
Just out and about - supermarket, Starbucks, on the train to work, etc. Weird, but I’ve never actually met someone interesting at a bar. I was infamous at work for my refusal to date anyone in the company, period, even if they were in another building/city/dept, but I was asked out by someone the week after she left the company.