"Jill of the Jungle" is an ancient DOS game, and honestly a bit sexploitative. But it does feature a female protag. And is old.
Patient Gamers
A gaming community free from the hype and oversaturation of current releases, catering to gamers who wait at least 12 months after release to play a game. Whether it's price, waiting for bugs/issues to be patched, DLC to be released, don't meet the system requirements, or just haven't had the time to keep up with the latest releases.
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Trails in the Sky FC and SC.
Also, FemShep was a popular option in Mass Effect for good reason.
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.
Yeah replaying all the RE now and it's crazy how this very early choice of two playable characters in the original series allowed the remasters to feel much more modern in their writing. Jill feels like the modern badass main woman a lot of game which they could write properly.
The Siberia series, King's Quest IV, Parasite Eve series, Excalibur 2555 AD, Fear Effect series
Phantasy Star. Love that game.
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.
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.
Metroid of course!
Also Ion Fury isn't old, but its made to look and feel old, and the protag is kick-ass
How in the world did y'all miss Silent Hill 3? It's October, and there are even other horror games mentioned. No excuse! Tsk tsk.
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.
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.
Siberia!!! And Dreamfall!!! Best games ever!!!
edit: also I saw Life is strange in the comments, this is a really good game. And also I remembered bayonetta!!!
A lot of point-and-click adventure games do feature female protaganists. One that comes to mind that's not bee mentioned so far is Kathy Rain.
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.