I know games-to-movies are virtually never good, but what are some you feel could maybe, just maybe work if the filmmakers actually tried and/or cared about the material?

Max Payne has already been tried and failed spectacularly in 2008 under Tom Rothman's Fox. It was a boring mess that had very little to do with the games from a hack director, but there's a fan-made short film on YouTube called Max Payne: Retribution that does a much better job capturing the look and feel of the games and actually has some good ideas sprinkled in there to boot. It's a 45 minute short, but you can tell the ingredients for a good Max Payne movie are there from somebody who actually cares about the source material (it gained a lot of buzz on the internet):

Uncharted.
The Last of Us.
Conker's bad fur day.

I don't think any really do tbh. FF7 remake was the game I felt most immersed in as a sort of anime movie. TLOU 1 is basically a retelling of Children of Men's plot line. So there's that. 

Never played TLOU, but I've seen Children of Men. Are you saying that TLOU is about how depraved humanity gets because of the mass depression that ensues from nobody having babies anymore, only to discover that someone is finally pregnant and we can all now stop killing one another?

That movie has never resonated with me more than it does now. Having a 9 month old (almost) myself, I cannot adequately describe to anyone in words the joy I feel when she giggles.

Games make bad films. TLOU would be a bad film. Any Cage game would be laughed out as the next Neil Breen. Games don't work as films. No AAA game esp despite their marketing buzzword of "Cinematic" is good enough or will work in a film format. So spouting Last of Us is stupid. What does work as a film is Sonic? Mario. Pokemon because they are so simple. It's easy to work around them.

Almost all games could work as movies depending on the director,investment.

I am sure any Nintendo character with a high budget like Detective Pikachu would become a successful movie.

The problem with game-based movies is their stories either don't translate well to the big screen, are too big to condense into a 2 hour movie (or 3 hour movie in the case of Skyrim, which I surmise is what it would be being it's fantasy and a massive fucking game) or the filmmakers just don't care to do them justice because they don't like/play the games in question or games at all or some combination. 

Even when a game that COULD fit into a movie is adapted, they often disregard the source material, anyway. Max Payne is practically already a movie in game format. Its story is so simple: it's about a cop who comes home to his dead wife and baby and starts spraying coked-out hooker-boning gangsters in bullet time effects. Sounds pretty simple, it's basically the Punisher, its cutscenes are literally comic strips FFS, yet the 2008 movie was a complete mess with almost no relation to the games whatsoever (the fact that it was watered-down is a whole other can of worms). Characters just walk around, explain things in a convoluted fashion, then disappear with so many plot holes, I'm surprised the cast didn't fall through them during filming. Oh, and there's no shootouts until the last 20 minutes or so and very little bullet time is actually used for the cherry on top.

Mass Effect is another one that could easily fit into a movie with the proper love and care for the material. Like I said, it's basically Star Trek meets Alien, you'd have to TRY to fuck that up, yet knowing Hollywood's luck with game-based movies (even ones that shouldn't be TOO hard to adapt), I'm sure they'd find a way, anyway.