Half Life 2 was the first game to have a proper 3d physics system implemented, and while it wasn't flawless, it worked. It allowed the player to grab specific items, and carry them around and throw them into other objects, which would react accordingly. This was shown off a lot throughout the game, since the developers were proud of it. Now, it has become commonplace for almost every game to have a physics engine, as it's called, although it doesn't have to be a main gameplay element.
The topic of physics is particularly interesting when you look at the most popular genre, first person shooters. Some games use a projectile to calculate where the bullet will go, while others just use a "hitscan" system. Hitscan is when the path of the bullet is determined as a ray, protruding directly from the player's gun. It could go perfectly straight where its being aimed but most of the time there is a small deviation. This method is simple but effective, as it allows for much faster calculations to be done by a multiplayer server. If the ray hits a player, do damage, if not it will either hit a wall or continue on to nothing. The projectile method actually launches the bullet and does all of the physics calculations for it, such as being affected by gravity and other such variables. This method is used by all of the games in the Battlefield franchise, and is an integral part of the gameplay. Because the fighting happens on such a massive scale, having the bullet travel realistically makes a big difference. Different weapons shoot with different initial velocities, and some have less gravity affecting them. This is used to make some of the weapons fair, such as being able to do more damage but having a much slower velocity makes leading and actually hitting the target much more difficult. The drawbacks of this system are that the server is doing hundreds or thousands of these calculations per second, and with up to 64 players on a server at once, it can be very resource intensive. For people with poor internet, it can result in some strange errors, such as a shot hitting you after you rounded a corner, or being hit by shots that clearly missed. Due to advancements in technology, these calculations have become more efficient, and the fact that we can create a relatively accurate simulation of that many bullets at once is an impressive feat.