I have to point out (seriously) that this question, as written, is heavily skewed towards Caucasians.
Posters/alien space bat victims who are obviously (physically) of an ethnic minority and who have spent all their lives in the U.S. or Europe have two choices:
a) Go to their homeland, where they’ll be discriminated against heavily, maybe even enslaved with the multi-century version, or
b) Go to the nation of their ancestry, where they don’t know the language.
Either way, they’re SCREWED.
I’m sent back to 1910? I’m headed straight for the nearest stockbroker. After I’ve begged, borrowed and stolen as much cash as possible. Then I pull it back out after making a tidy profit and go live a life of luxury.
I’m a woman, so I can’t vote and I have no rights. I can’t even own property. I’m going to have to marry some asshole.
Forget it, I’m not going to any time before Women’s Sufferage. 
ETA: Yeah, I’d probably just look up my great grandparents on the old homestead in Ohio and make friends with my grandfather, who would have been a toddler about that time.
It wasn’t clear that you wouldn’t have time to prepare mentally – just that you couldn’t prepare anything to go with you.
In any case, I’ve answered your initial point – which others have made in fiction over the years. The reason you see people absurdly prepared for their time traveling is that it makes a better story. I could buy Hank Morgan being ready for it, because he was a “hands-on” foreman in a factory, but even I have to give him a large Suspension of Disbelief for knowing the exact date of a solar eclipse in 6th century Britain (and being sent back to just that time.) I find de Camp’s story more believable because his hero doesn’t know such things (except for one key historical incident, which is pretty much the point of the story). His character gets tossed unexpectedly into the past, as in your hypothetical example, and he can’t actually do all the things he would love to be able to do – his efforts to create gunpowder fail, his mechanical telegraph is ignored. He doesn’t know how to make paper --= but, knowing that paper can be made, he eventually figures it out. His real contributions turn out to be unexpected things like double-entry bookkeeping (for finding accounting fraud) and distilling brandy.
As for turning pop-culture stuff into something valuable, Heinlein’s time-traveling heroes in Farnham’s Freehold are able to sell versions of popular games (requiring no more than boards, markers, dice, and cards). I’m sure that an awful lot of people will be able to remember things from their experiences that CAN be put to use in the past – they can make pottery strainers and colanders. or different types of tools than exist in the past they’re sent to – hacksaws, maybe, or saber saws. Claws for pulling nails. Maybe they’ll introduce the wheelbarrow wqhere it didn’t exist, or toothed gear transmission of power. Clothing styles. Different ways to lace up or attach shoes. Hats with bills like baseball caps. There’s no end to ideas one might introduce outof their usual place.
Whether or not you can effectively introduce them, or get hold ofg the materials, money, and labor needed, is something else entirely. Hank Morgan conned his way into power with his eclipse bluff. Padway was able to talk and finagle himself into a sponsor in exchange for a split in the profits. To be successful in the past you’ll need a pushy personality, interpersonal skills, and an ability to talk. Just having some random knowledge from the future by itself is no guarantee of success, but I think that not being able to build a radio from scratch (like Cabot in Ralph Milne Farley’s “Radio Planet” series) wouldn’t be a bar to success, either, if you had the right other skills and a decent memory.
Mine may be a little mundane but it would certainly work and would be interesting to me. My hometown was remarkably unchanged from the early 20th century until I was in high school. My family owned the local hardware/general store starting in 1902 and we still had it when I was younger. I would just go back to my hometown and find my family and hang out with them. I even knew my great-grandmother who was born in 1889 when I was a child plus plenty of other people who would have been alive in 1910 as well. I know plenty of family history so it shouldn’t be very hard to convince them plus it should be apparent based on appearance. Once I established that as a base, I would work on screwing around with technology and investments.
I’d make a terrible time traveller.
I know, I’ve done it before. I’m pretty much the one responsible for what you see before you today.
QED.
Men have a big advantage over women in this scenario, too.
I heard that people who had gotten the 1918 flu were immune to last year’s swine flu. IANAImmunologist, but mightn’t it work the other way, too? If you had swine flu or a swine flu shot last year, you might have some protection against the 1918 flu.
Now, smallpox, that most people today aren’t immune to.
You might also have to worry about other diseases that existed earlier but have since died out. In 1510, you might encounter the English sweating sickness, for example. We don’t know what it was, but most modern people probably haven’t been exposed to it.
As a (former) locksmith I imagine I could have a pretty lucrative career in either that field or as a professional burglar.
I knew it! Back in your time machine mister. You have a whole lotta fixin’ to do!
I agree with Little Nemo’s main point. Most of us have neither the skills or specific enough memories to take advantage of our civilization’s historical development.
Just for example, I’m a working chemist, but am highly dependent on glassware and reagents produced by other people, not to mention instrumentation. I’m not sure I could do much better with 1910 era chemical equipment than the people of the time.
I could point out the upcoming revolution in quantum mechanics and astronomy, but lacking the math skills to make specific predictions is a sure road to nowhere in science.
16th century? I could possibly make some contributions in metalurgy, but gaining the credibility to go beyond apprentice level would be a lifetime undertaking.
My $0.02: people who show up the history books have a unique combination of ability, interpersonal skills, and drive. Great ideas help (obviously), but are only a piece of the puzzle.
Walt
I don’t know how to build a steam engine, exactly, either. But I understand how to do experiments, and I know that you can build a steam engine, and so many basic mechanical and engineering concepts, and I think that’s worth more than you give it credit for. Given even a little bit of traction, I’d be one of the greatest engineers of the 16th century.
Hell, just knowing how to dress a wound and sterilize things with heat or alcohol would make me the greatest doctor who ever lived.
There are still major problems with fitting in enough with the culture to get people to believe you’re not just some nut (or demon), and not starving long enough to have a chance to build something and start selling it, but I think people vastly underrate the value of average modern knowledge.
I think the England of 1510 would be a very interesting place to go. With young King Henry VIII on the throne, a man of noted intelligence and ideas. Just don’t get mixed up too much with the Church. 
This makes all the difference. Even without mental preparation I’d be at some advantage in 1910. My vague concept of technological history combined with newspapers of the time would help me understand what the good investments are, but realistically I don’t remember who won what sporting contest in year X, so I wouldn’t make a gambling fortune. That said, this advantage is heavily offset by being completely out of my depth from a social point of view. How do you get your first job when you are a complete freak?
If I had some time to prepare gambling wins become more likely. Also, some research into profitable oil, gold or other mineral strikes might lead to buying profitable land while it is still very cheap.
1910 - I would prefer a rural area in some basically English speaking region. I grew up on a farm and I practice Living History as a hobby so I could do fairly well in that setting. I don’t want to do too well - I want to avoid undue attention. Which is part of my reason for wanting to stay out of cities.
1410 - drop me almost anywhere. People were beginning to travel more and there was a distrust of “foreigners” but not the hatred one sees later (for the most part). Given a culture/society such as France or even a stone age culture such as among the pre-Columbian Twigtwees, I could manage fairly well.
I would be a terrible time traveler. My only advantage in 1410 is that I can read mensural notation and know a bit about Italian music of the period (just finished taking a class on it), so I’d probably pick someplace in Italy and try to be a musician. I doubt it would go very well, though - I’m a woman, I don’t play any period instruments, my Italian is awful, etc. I’d probably die within a week.
1910, I guess I’d go to New York or Boston or something and find a gay man to have a sham marriage with. Get involved in the classical music scene, maybe teach music lessons, try not to die, hate not having all the rights I’m used to. I doubt there’s any money to be made in making predictions about classical music, but I could do a lot of that.
I have no scientific, mathematical or engineering background. But I agree with the above. I think if I were transported back to 1510 I would be able to make such a huge impact it would be unbelievable.
No. I have no clue how to get a steam engine to work. I don’t really understand the electical needs necessary for light bulbs to turn on.
I also don’t understand the details of plumbing but I know what indoor plumbing is and can probably rig up an awesome system. I can take it one step further and create an entire citywide sanitary system.
Handwashing! Not really a new concept, I know. But imagine if doctors used that before operating? I think I could cut the death rate in half.
So along those lines, think of all the little bits of knowledge we have that would make a huge impact to people 500 years ago simply because no one back then even thought about the concept.
If you’re worried about alien space bats taking you back in time, you may want to print this out and keep a copy handy in your backpack, wallet, or purse.
In 1910, there wasn’t a whole lot of slavery going on. With a modern educated American accent you could be popular and exotic, instead of simply one of those people.
Not sure about 1410, but I thought in those days people who could pass themselves off as educated and from the upper class of wherever they came from could get along fairly well. It might take a lot of bullshitting, explaining why you don’t speak your native tongue, etc.
But why would they listen to you? It took Ignaz Semmelweis YEARS to convince doctors that maybe washing the gore of a post-septic autopsy off their hands before sticking their fingers inside the next laboring mother might just cut down on childbirth fever, and he was a respected physician in a well run clinic in Vienna.
(Hell, to judge from many docs I see in the hospital today, the memo is still making its way around.)
And not half…try twentyfold! Handwashing IS crazy important, it’s just a really hard thing to convince people of.
So go back and fix it.
As for the starting premise, I’m an insulin dependent diabetic. Unless the alien space bat can CURE me, I won’t have to worry about what to do. Insulin wasn’t even discovered until sometime in the 1920s, I think (too lazy to Google right now). Without insulin, I will become very sluggish in 24 hours, and won’t be able to do anything. I don’t know how long it will take me to die, but it won’t be too long. And it doesn’t matter if I completely eliminate carbs from my diet…my blood sugar is going to soar, and I’m gonna die.
If the ASB can cure me, I’m still female. And that means that I’m pretty much limited in what I can do…at least, if I want to profit by it. Women couldn’t even file patents for a long time, they had to have a male file patents for them, but I’m not sure if they could by 1910. Women were literally second class citizens, and had problems functioning independently. For the most part, their fathers or husbands or brothers took care of their business needs.
Boil the water before you drink it. Might not have to do that in 1910, but definitely do it in 1410 or 1510. Boil it for at least 10 minutes. If you could get someone in charge of an army to listen to you on this, you could reduce battlefield deaths as late as the US Civil War. More men died of diarrhea than of bullets in the Civil War.
The recipe for oral rehydration solution would probably be a useful thing to memorize. 1 teaspoon salt, 8 teaspoons sugar, 4 ounces of orange juice if you’ve got it, and 1 liter of water. Don’t forget to boil the water first.
You know what prevents scurvy. That would be useful to anyone who deals with ships.
If nobody else speaks your alleged native tongue, either, and nobody is likely to have heard it, just say whatever you want. That’s what George Psalmanazer did.
1910 is fine. I have some basic knowledge of the era and language isn’t an issue. New York would be a good location, especially once I scare up some money to invest. There were hundreds of car companies all starting out; I’d be able to pick the winners. I could make do by writing fantastic fiction for** The Argosy** until I had a nest egg.
1510 is a little harder. I’d aim for somewhere in England, probably London.