Max Payne (2001, Playstation 2)

Max Payne is an action game and third-person shooter originally developed by Finnish company Remedy Entertainment and 3D Realms for the PC. It was ported to the PS2 by Rockstar Canada and published by Rockstar (in North America, Europe and Korea) and Electronic Arts (in Japan). The game also came out for classic Mac, Xbox, Xbox 360, PS3, Android and iOS. A Dreamcast version was in development, but got cancelled. A modified version of the game was developed for Game Advance, replacing the 3rd-person real-time 3D with 2D isometric graphics, but keeping the game mechanics the same.

Max Payne is a New York Police officer whose life is shattered in an instant when a group of criminal junkies brutally murder his wife and bay daughter. The killers were users of a new dangerous drug called Valkyr. Max is determined to bring down the mafia family who is responsible for selling Valkyr in New York and becomes an undercover agent, infiltrating the mafia. One day Alex, one of his current few contacts within the police asks to meet him in the subway. Upon arrival, Max does not only accidentally stumble into a large mafia operation, an unknown assassin kills Alex and frames Max for the murder. With the police on his heels and nothing left to loose, Max becomes a vigilante and starts a brutal one-man crusade against the mafia.

As far as I know, Max Payne was the first game to introduce the "bullet time" feature. You can slow down the action to slow motion while aiming at regular speed to mow down groups of bad guys. Bullet time last as long as the hourglass guage not fully depleated, and you can also end it deliberately by pushing a button. The hourglass will slowly refill while you are not in bullet time. You can jump-dash forward, roll to the side and jump, also in bullet time. Max' health is displayed via a pain meter. You can take painkillers in order to regain health.