The first game of the series was released in 1993. It has eight selectable characters and one unplayable boss character, Oume Goketsuji, a palette-swap of Otane. Originally, every character had a specific win quote for each defeated foe, but that was reduced to only one win quote for each character in the English version.
This game was ported to Super Nintendo and Sega Mega Drive/Genesis and included some new play modes: Vs. Battle, Practice Mode, Time Attack and a "Life Attack" that consists of defeating as many opponents as possible with just one life bar (similar to the Survival Modes seen in other fighting games).
The Mega Drive version had a Battle Royal mode where 1 or 2 players can select a team, with an option to hide the characters being chosen and they would not be revealed until during gameplay. Additionally, it featured an option that allowed the strength of each special attack of every playable character to be adjusted to the player's liking.
The English console ports of this game had several omitted features, such as Karaoke Mode with the lyrics for the songs "Tatanka no Uta" and "Otoko no Karatemichi", character biographies that popped up in between demos, the intro demo to the game and the scene of Oume where she speaks to the player before she fights them (which changes if she's fighting Otane).
Another difference between the American Super Nintendo and Japanese Super Famicom versions are the endings; the Super Nintendo version replaces them with a Congratulations screen with the character portraits used in the pre-fight screen, while in the latter the endings are still present, though slightly different from those in the original arcade version, drawn in a style similar to the endings found in Power Instinct 2.
Source: Wikipedia, "Power Instinct", available under the CC-BY-SA License.