Around 4-5 I stopped letting them win, but I still don’t always play my best, especially if it’s a new game I’m trying to teach them.
My oldest was a terrible loser when she was little. We used to play via dolls, so that it wasn’t her that lost, it was the doll.
This.
I never let a kid win on purpose. When they do win, they know they have achieved a genuine victory.
My parents never let me win. When I finally started catching up to Mom in Scrabble it was really something. When I finally beat her, I was ecstatic.
I’ll let really little kids ‘win’ sometimes but past age 3 or 4… nope. Of course I’m not trying to make small children feel bad, and I always play as a ‘team’ and provide advice to my 7yo nephew when we play games that are difficult/too old for him with his sisters who are 11 and 13. And I don’t play things like checkers with little kids, I can see letting them win at things like that until a much later age.
I think learning how to lose gracefully and learning from the effort and techniques others use to win/excel at something is really valuable for kids starting young. I know way too many kids where the adults in their lives bend over backwards 24/7 to make the kids feel like they are the best at absolutely everything I do, and it seems to create really bad situations when the kid finally comes up against a real-life situation where it’s clear they aren’t the best and they can’t win. It can also contribute to entitlement and brattiness.
I also think it can be a bit insulting to a child’s dignity and intelligence to always let them come out ahead of you. Not always of course. I’m not trying to imply letting your kid beat you at checkers every time you play means you’re a bad parent or your kid will turn out to be crippled for life or an asshole.
We never let them win. For really little kids it’s just chance, anyway. The first time my younger daughter had a fit because she lost a game, I said, OK, let’s play again and this time you’ll win. We positioned our markers at the starting point. I immediately moved hers to the finish line and cheered, “Yay! You win! Wasn’t that fun? Want to play again?” Repeat. “No, Mommy, I want to really play the game, not just say ‘you win.’” Really? Which is it? If you actually want to play the game, you might win and you might lose. She got the point instantly.
Now, if it was a game where she reasonably might be at a disadvantage because of her youth, we did make special handicapping rules. For example, when we played Big Boggle, the adults had to make words of four or more letters, but the youngster could also score for three-letter words. And we adjusted the points so that she got one more point for the same number of letters as an adult. We stopped that after a few years when she got to winning ALL the time!
I think it depends, it’s OK to cheat to lose if you’re helping them in the long run. No kid is gonna like to lose 100% of the time, so you have to keep him/her interested.
For me, it depended on the game.
The Kiddo was not quite 4 when he first asked me to teach him chess. By 5, I didn’t have to let him win, we were evenly matched. Now, at 12, I think he lets me win sometimes.
Other games, I just tried to play to match his skill. Sometimes he won, sometimes I did. Kids don’t learn if they always win. They also won’t want to play if the always lose.
About 4. After that the kid’s old enough to understand the concept of handicaps - giving them some extra points to start with or whatever, if that’s necessary for there to be any element of competition.
Depends what the game is, anyway; my daughter’s been beating me at swimming races since she was 10 and beating many of my friends at running races since she was a toddler. 
Little kids also have magic powers when it comes to video games.
It depends on a lot: physicality of the game, how many times in a row I’d already won, etc.
I find it hard to believe that there are parents here who have never let their kids win? WTF? So, when little Billy (more likely Tyler, or Jacob) wanted to play, say air hockey with you, you tried your hardest and beat him 498 - 3 every game? That’s gotta be fun for the kid.
I can usually give it my all now for every game, but sometimes you let up a little and give the kid a sense of accomplishment. I mean, their happiness ans self esteem goes up a notch and you get a sense of vicarious accomplishment too.
I think you’re assuming I’m a lot better at air hockey than I really am. 
No, as said upthread, most little kids’ games are luck based, not skill based. I let luck lead, and sometimes I win and sometimes she wins. And sometimes, we play these awesome hippie crack cooperative games where EVERYONE wins. Whee!
Don’t you ever do that trick where, to get them to hurry up, you say ‘last one to the car’s a wet banana!’ (or whatever)? Then race them in a silly way and either win and go ‘nyer nyer, I beat you, you’re a wet banana!’ or pretend that you’ve got caught in a time-loop and run in slow-motion (saying 'nooo Iiii’mmm loooosssinggg) so that they can win?
Or similar stuff. Letting them win is sometimes part of the game.
lol. No, not really. Daddy’s the silly one who does fun stuff like that. Mama’s boring and makes you hold hands while you cross the street and check both ways for cars. 
I have no problem with that sort of “letting them win”, I just wasn’t considering it in the context of the OP. I guess I do let her “win” when we have contests to see who can get ready for school faster or finish all their peas, though. 
The Firebug’s 3, and I don’t automatically let him win. What I do is find ways to tip the odds his way, so he wins most of the time, but loses some of the time. I’ll probably tip the odds less his way over time; I doubt I’ll be giving him any sort of edge when he’s in second grade.
My solution to keeping Candy Land from going on forever has been to draw a number of additional shortcuts into the board. Having just two, both early on in the board, made no sense to me, so I added five or six more in obvious places. That tips the odds more in favor of progressing on the board, and we almost always finish the game before going through the deck once. Since that’s about at the limits of the Firebug’s attention span, that’s a good thing.
I taught my son chess when he was about 3 or so. I would show him how the pieces move, and what his best strategy would be, and even what I was intending to do, as the game progressed. At first, I would make simple, obvious moves, and I explained how to best defend against them, but I would always win. As his game improved, I would up the challenge, until, at about 7 or 8, he could actually beat me on his own.
My dad, however, would make essentially random moves, and my son would always “win.” When he saw me winning against my son, he’d say, “I bet you feel like a MAN, beating a six-year-old!” in his sneering, disdainful way.
When my son could regularly beat me, he felt so PROUD! and rightfully so. I am a very accomplished player. He understood I was good, and he got so he could play any of the kids at school, and never lose a game. They stopped playing him, because he’d always win.
Did he learn chess more from me, or my dad?
That’s a pretty nice description of what I do. But I also might, if the child is constantly losing, intentionally make a bad choice or two.
I also had a psychologist back when I was 8 or 9, who would play chess with me, but never make a capturing move unless I made one first. I thought I was getting really good at the game, until I fell for the fool’s mate in a tournament. Heck, the best I did was in one game where I played like he did, intentionally not trying to win, and got everything down to two kings.
So, even if you tend to let kids win, I’m a big supporter of at least sometimes beating them, so they can learn to get better.