Patient Gamers

Okami

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.

Ms. Pacman :)

The Guardian Legend on NES.

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.

Wet is a fun game if you can handle the loading screens.

Cult: Heretic Kingdoms

Fantastic RPG game, with a badass female protagonist.

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

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

I'll recommend a few from different genres:

• Fire Emblem: The Blazing Blade (later FE games also allowed the player to choose between male and female)
• Castlevania: Order of Ecclesia (or Bloodstained: RotN for a newer, but aging, game)
• A Hat In Time (not sure if this is really that old but it's an amazing platformed)
• any Touhou game
• Life Is Strange (again, not sure if you'd consider this old)

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.

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)

• Broken Age - point & click
• Little Dew - ARPG/Zelda-like
• most RPGs with character selection (Elder Scrolls, Mount & Blade)
• Raven's Hike - puzzle/platforming
• Shantae - platformer

I don't think anyone has mentioned this yet.

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.

Venetica

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

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