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

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.

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)

Ms. Pacman :)

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.

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.

• 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.