There's a variety called "Elfie" that my mother has declared the best frying potato ever. She keeps reminding me to make sure to grow plenty of them next year, even though planting season is months away.
"Pinto Gold" is a good soup potato. It tends to be small and smooth-skinned, which makes it easy to just toss some in whole. It would probably do well in potato salads, although the color from the skins sometimes bleeds into the flesh and looks weird.
My favorite mashing potatoes are the gold-fleshed, waxy kinds. I know most people prefer the floury kinds, but to each their own. I really like "Redgold". It did fairly well in my garden this year. "Yukon Gold" and an unnamed variety from the grocery store were both good, too.
I tend to treat baked potatoes as mashing potatoes with skin on, so I don't have any variety just for that.
"Red Pontiac" did outstandingly well this year, and it's a good all-around potato, in my opinion.
I grew a fingerling variety this year that wasn't so good. It produced very well, but about every 3rd one was so bitter it burned my mouth! I ended up composting them rather than deal with that. Unfortunately, it didn't have a variety name on the label, just "Fingerling". It looked a lot like "Russian Banana", but there's no way to tell for sure.