If you accept games where you fully create the character, you've got a ton of RPGs. Baldur's gate, elder scrolls, arcanum, fallout.
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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No One Lives Forever (and 2)
It's also rare to have a female protagonist in an FPS.
Ms. Pacman :)
Super Hang-On had a female protagonist but you only found out if you beat the hardest arcade mode
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.
Cult: Heretic Kingdoms
Fantastic RPG game, with a badass female protagonist.
Metroid!
Wet is a fun game if you can handle the loading screens.
Venetica
A roleplaying game with a female hero and an interesting story:
https://store.steampowered.com/app/338140/Venetica__Gold_Edition/
another classic i totally forgot existed, thanks for reminding me
- 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.
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)