Highwayman.
What I meant was if you were born from the parents you have now, but 500-1000 years earlier. Some parts of you would remain unchanged: your gender, social status, sexual preference, health, interests and all that, but no knowledge of contemporary ideas. So I would still be a gay male, with no interests in crafts or manual labor, but with interests in the working and history of the world. I would not however know what an atom or electricity is, and my computer skills would most probably translate to some sort of scribe skills. Since I would be born to a family with not much money, I would not have had access to any education or had any good chance of being apprenticed to skilled worksmen.
And as Nava mentioned, you’d have to have the cutoff at some point. Let’s just assume you survived childbirth, otherwise more than half of the posters here would have died of some complication or infection or such.
By the odds, I’d be a farmer.
By choice, silver or goldsmith. Maybe a potter or glassblower.
I have pretty good mechanical skills, so a blacksmith might be a good calling for me, or certainly a scribe as a good writer and a person with good handwriting. I also like long drives and have often joked that if my proposal writing job didn’t work out, I could always be a truckdriver.
Whoever the guy was that was responsible for riding horses long distances with or without wagons to deliver supplies would be a great job for me. I also don’t get seasick, so let me be the first to suggest merchant sailor/fisherman…or privateer…
Merchant class. My father was a merchant (traveling sales), and I am in marketing and sales - probably be doing the same.
I would have lost my current wife and son in childbirth (emergency c-section for a cord wrapped around the neck did not have a huge chance of success).
Hopefully some sort of guild artisan: tailor, baker, brewer, printer, metalsmith come to mind.
I’ll say printer. I’d’ve liked to apprentice to Gutenberg or Manutius and be in on the birth of typography.
Town Crier or Innkeeper.
My former profession was broadcasting.
I enjoy being in a social setting with people.
Although with my 6’7" frame, innkeeper would probably be more likely, as I wouldn’t need a bouncer.
Heck, I am a geologist now. Guess I would have been playing with rocks back then also.
With my ancestry intact I would have been born into an offshoot of the royal family at the time. Unfortunately not everyone in the royal family was rich so I have no idea what my economic status would have been.
As a woman in the Chosun period I would have been married off into another family of the gentry and would have been expected to engage in feminine activities such as painting, embroidery, poetry, etc. I suppose I could have run away and become a giseang (geisha) if I’d been so inclined. In some ways the women of the lower classes had a lot more freedom - the women of the scholar-gentry were mostly expected to sit quietly and look pretty. If I were very ambitious I suppose I could marry a high ranking official and participate in golitics through manipulating him.
Without modern glasses or contact lenses I would be legally blind. Even if corrective lenses existed in some form 500 years ago the chances are I would be born into a family that could not afford them.
I’m guessing I would die very young, or be some sort of beggar. It makes me appreciate living in current times. What could have been a horrible affliction is nothing but the most minor of inconveniences.
If I had good eyesight I am not sure what I would be. I’m a software engineer by trade and pretty mathematically inclined. I expect I would do well in academia, but weren’t such opportunities very much based on the standing of your family? If your family was poor, I thought you just did whatever it was your father did to survive.
So, farmer. 
Currently a Programmer but due to other skills and mindset I think I would have been a Sailor and/or Carpenter.
If we translate from what I do do now, I’d be working as a…well, hell. Hrm. Being female, little translates, since women didn’t do squat, did they.
Bugger that for a load of carp.
I’mma be an outlaw.
Can I leave my farm, husband, and 15 kids and go outlawing with you? I’m tired of birthin’ babies.
Absolutely! We can roll johns in the jakes…or is that jakes in the johns?
I should not speak for others, but I suspect many of the people on the SDMB would have become some form of Goliard, wandering scholars who composed such works as the Carmina Burana. They were often schooled by the church, literate, itinerant, and survived by going from place to place bartering their useful skills (chiefly reading and writing) for food, drink, coin and possibly sometimes sex. Many would have been monks if they would have taken the vows of poverty and chastity, but they seem to have found those vows unappealing…
If you are really talking about 1510, I could well have been a singer/lutenist (or vihuelist) back then as well. Earlier than that, well, I probably would have ended up as some kind of church musician/monk/goliard.
Wait, what? I can trade reading and writing for sex? I want to change my answer.
I have never wanted to be a nun, but the lifestyle of a wandering monk has always appealed to me.
This despite being female and non-religious.
Maybe I could have just kept my mouth shut and my boobs strapped.
I’d probably have been a priest.