Patient Gamers

If you accept games where you fully create the character, you've got a ton of RPGs. Baldur's gate, elder scrolls, arcanum, fallout.

Okami

No One Lives Forever (and 2)

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

Ms. Pacman :)

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

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)

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

Cult: Heretic Kingdoms

Fantastic RPG game, with a badass female protagonist.

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

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.

• 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/

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)