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.

Metroid!

No One Lives Forever (and 2)

It's also rare to have a female protagonist in an FPS.

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!!!

Saboteur 2 https://en.wikipedia.org/wiki/Saboteur_II:_Avenging_Angel

Cult: Heretic Kingdoms

Fantastic RPG game, with a badass female protagonist.

Eien no Filena on the SNES/SFC (it was Japan-only but it's been fan-translated).

Not only is the protagonist a woman - that fact is repeatedly plot-relevant.

The Guardian Legend on NES.

Ms. Pacman :)

Final Fantasy 6. There are technically several protagonists, but the one with the better claim to "main protagonist" is a woman.

Also, Heaven's Vault isn't an old game, but it's not very well known or talked about, so I'll throw it in anyway.

Super Hang-On had a female protagonist but you only found out if you beat the hardest arcade mode

Erica

The Syberia Series

The Longest Journey

Gone Home

Virginia

What remains of Edith Finch

Beyond Good and Evil

Gabriel Knight 3 has shared protagonists that you switch between; one is a woman.

Likewise some of the Broken Sword series

Talos Principle is either non-gendered or whatever you want the protagonist to be.

The first Blair Witch game from 2000

Everyone's gone to the Rapture

Also, holla at whoever said "No One Lives Forever"; that game rules.

Venetica

A roleplaying game with a female hero and an interesting story:

https://store.steampowered.com/app/338140/Venetica__Gold_Edition/

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)