I remember creating a female Twi'lek Jedi in some of the old LucasArts Jedi games.

• LucasArts Jedi something something
• KOTOR
• Baldur's Gate
• Fallout Although these were more like "create-your-own protagonists" rather than "known hero protagonists" that people recognize.

Aside from the classics already mentioned in the thread, Lara, Chell, Samus, Valentine, Redfield, etc. here's a few that come to mind:

• Peach in Super Mario 2, the game that feels more like a mushroom trip, than a trip to mushroom kingdom
• Aya from Parasite Eve
• Chun Li from Street Fighter, also Cammy
• Mortal Kombat
• Tekken
• Soulcalibur
• Dead or Alive
• Sarah Kerrigan in Starcraft(s), although it's an RTS, so protagonist is a bit loose.
• Rayne from BloodRayne, the first video game character to appear in PlayBoy, eh
• Ellie from The Last Of Us, damn it's been 10 years already? Is that an old game already? Am I old? Nevermind, don't answer.
• Clem from The Walking Dead
• Joanna from Perfect Dark

I'm sure I'm forgetting a few others.