How old are we talking? Final Fantasy VI, Super Metroid, Resident Evil 2, and the OG Tomb Raider series are all pretty old but great.
Portal, Portal 2, Mirror's Edge, Alien Isolation, Child of Light, Celeste, Tales of Berseria, Final Fantasy XIII, Slime Rancher, the newer Tomb Raifer games, and A Plague Tale are a few games from previous gens that hold up really well.
A more recent game that flew under a lot of people's radars is Kena: Bridge of Spirits, and it was a lot of fun. Also, Atelier Ryza and Alba: A Wildlife Adventure are very worth mentioning, too. :)
Tomb Raider (1996). The levels are well designed and work with the tank controls in a way that lets you master Lara Croft's acrobatic descent through haunting environments that feel far more threatening than most games I see today
King’s Quest IV: The Perils of Rosella
One of my most favorite King’s Quest games. And one of the first games I remember playing with a proper female lead.
The Longest Journey was my favorite as a kid. Point and click adventure about a young art student in the future who keeps teleporting to a fantasy world.
Jill of the Jungle is the oldest one I know of that isn't Metroid. Fairly certain Metroid was first, but everybody knows Samus. Nobody, even people my age, ever talks about Jill of the Jungle tho.
Iji is a free game released in 2008. Sidescrolling shooter with a story, fun boss fights, and a great soundtrack. It's really a shame it isn't as well known in these circles, it's quite good.
Trying to think of some obscure, unknown games: Eien no Filena, a JRPG on the Super Nintendo. The protagonist is a woman pretending to be a man as a lower class citizen forced to be a gladiator. Awkwardness ensues when she is "assigned" a wife and the men around her start being very confused about their sexuality.
I put together a list of games for every letter of the alphabet with playable female characters that I've personally played and a lot of them are pretty old.
The main protagonist in Final Fantasy 6 is female. There's a large number of games that age or newer with Female protags... older is a bit harder (but not too hard. You just unfortunately end up with a lot of fringe games or exploitive games)
And below, some cheatiness (a fairly exhaustive list of both :) )
The older Resident Evil games (1, 2, Code Veronica, RE:Zero) have playable female protagonists. Actually most of the RE games have at least one segment where you play as a female character.
The swapping of two protagonists is actually something I wish they would bring back to the modern games in the franchise.
At risk of posting twice but, I had to add this one as well:
Kyrandia 2: The Hand of Fate
A point-and-click adventure game. It was funny, colorful, and Zanthia is still awesome :) Made by Westwood of all people. It makes some references to the first, but you could play it on its own.
Donkey Kong Country 3 if you count anthro characters. Dixie is also in DKC2 but there she is the sidekick and not the main character, not that there's much difference from a gameplay perspective.
I haven't seen it mentioned so i'll go with Ion Fury. It's not really that old, but it's made on Build engine. The same was used in Duke Nukem 3D or Blood. Same roots means main protagonist have badass comments on lot of game occasions.
Don't know if PS1 counts as old but Valkyrie profile is one of my favorite games and you play as a Valkyrie recruiting fallen warriors and training them up for Valhalla.
Star Ocean 2 (also on PS1) is another one of my favorites and you can choose between a guy or girl at the beginning, which changes the story a bit.
Napple Tale: Arisa in Daydream
A game for the Dreamcast that had a primarily female dev team. It was exclusive to Japan, but a translation patch was released a couple years ago.
Atelier series
There are a bunch of these. They’re RPGs based heavily around crafting. Actually, they basically pioneered crafting in RPGs.
Um Jammer Lammy
A spin-off of Parappa the Rapper. Lammy has only 15 minutes to make it to her band’s performance, but getting there won’t be easy.
Note that Stage 6 is censored in the North American release. Also as a bonus, completing the game unlocks Parappa mode, with new versions of every song after Stage 1.
Athena
Stick with the original arcade version. The NES port is infamously bad.
Psycho Soldier
A spin-off of Athena (sort of) starring Athena’s descendant/reincarnation (it depends on the writer), Athena Asamiya (and Sie Kensou as player 2’s character). Athena (and Kensou) would later become staples of the King of Fighters series. The game is notable for being the first game with a vocal soundtrack.
Baraduke
An arcade title from Namco. Being on this list is actually a pretty big spoiler because the fact that the protagonist is a woman isn’t revealed until the end of the game. Now that probably sounds like a ripoff of Metroid, but here’s the thing: Baraduke did it first.
Koudelka
An obscure horror RPG for the PlayStation.
The game is an unhappy compromise between the creator and the dev team. One side wanting to make a survival horror game and the other going for something like Final Fantasy VII. I’ve never actually gotten very far in this one because I hate the battle system. Also, this game has connections to the later Shadow Hearts series.
Literally every game in the Otome genre
Probably not what you’re looking for, but technically fits your criteria of having a female protagonist.
I might add more to this post if I can think of something else.
Most of my suggestions were already mentioned, but PN03 & darkened skye come to mind.
Pedantry aside, if you count the option of selecting a female character, trickstyle, borderlands, super mario bros 2, vigilante 8 second offense, tony hawk 3 (4, underground and probably any in this series but I haven't played them lol)
One of my top 3 JRPGs, Star Ocean: The Second Story, has a remake coming out early November. In the beginning of the game, you get the choice to play as one of the main characters, a male or a female, each of whom has their own story arc and exclusive party members that can be found during the playthrough.
Actually not from older generations, but Tacoma and Deliver Us The Moon are a few years old and both are short, sweet space-related narrative games with a female protagonist.
another game I played (forgot the name, will edit later)
most games where you could choose between 2 or more playable characters
Now that I think of it, the only not oversexualised female protagonists in retro games (I can think of rn) are from japanese titles. The USSR didn't import video games and Europe and the US were just too conservative ig.