I tried searching for this game online, but since I can’t remember the name of the game, I’m coming up with zilch. I know you guys will make me smack my forehead, saying “That’s IT!”, in record time.
Here’s what I remember: sort of a 2D tournament fighting game. You can create your fighter, male or female, and choose hair, clothing and general look (basically, by clicking through - you can’t specifically choose the look from a list of choices). Your starting attributes, skills, weapon and even a pet are assigned at random when you first create your character, and as you level up.
You fight in turn-based fashion, but it’s basically choose an opponent and start the fight - you don’t actually control your fighter. One side will go, wherein your fighter runs over to the other fighter and strikes it in some fashion, then the other fighter will run over to yours, and so on, until one of you runs out of health and loses the fight. You can only fight three fights in a 24-hour period. The winner of the fight either holds aloft the weapon in hand or a triumphant fist, while the loser kneels for some reason.
I remember the pets the best: you can get one or two dogs, a wolf, a panther (which looked just like the wolf, as I recall), or a bear. Sometimes, if luck goes your way, you could get multiple pets.
As you level, you may get some points in attributes (I think there are three of them), a new skill, a new weapon, or (rarely) a pet.
I played this game like crazy two or three years ago, having a few dozen fighters, but my CRS (Can’t Remember Stuff) disease is quite advanced these days. 
Okay, hopefully I’ve given you all enough to go on. Starting the clock…now.
