Chases, especially car chases are an action movie staple, but few rulebooks seem to cover them at all, and if they do they cover them poorly. I find this regrettable.

How do you run car chases in your games?

My thoughts towards rules for them are here.

My favorite car chase rules are unquestionably the James Bond 007 car chase rules. However, I've never seen them adapted well outside of that game.

I do appreciate that Savage Worlds (my current go-to universal system) has a well-thought out chase system. It's not my favorite, but it's at least workable.

My go to on any chase is Call of Cthulhu. It doesn't matter if it is a foot chase or a car chase or what ever.

The basis is make a Con check. The lowest result(s) get one move point. the highest gets something like 3 points. The GM lays out a series of points (can be straight line for a simple race, or it can branch into to or 3 option paths, or it can be a complex grid. The target starts 3(ish) points ahead of the chaser. Everyone can use their point(s) to move or make a skill check or attack or what ever. 1 point one action. Some points have an obstacle there so it takes a point to move to it and a point to do the skill/attribute check (spending extra time/points gives a bonus to the check). The PC can choose how they want to try and overcome the obstacle. Do you use a locksmith skill to pick the lock on the door, a STR check to kick it in, an observation to see if there is an open door or window further down, or a climb check to climb up to the 2nd floor etc. Once you get to the end of the grid (and if you are at least ??2?? move points ahead) you escape / win the chase

Now take it out of a foot race into a car chase. Make a drive skill check (I'd modify it with the quality of the car). Lowest result gets 1 move point, highest gets up to 3. Make the grid etc and put different checks in the route. Skills can be drive, navigate, spot hidden, dex checks, and then combat skills etc to shoot at the opponent etc.

I used this in a WW2 / CoC one off for the PCs to try and run away from the ghouls and demon dogs that were chasing them out of the pyramid. they had to spot dangers ahead (to have a bonus to make the check) navigation to not get lost, drive checks to speed across an extra point etc. They got stuck once and had to make a mechanical check and str check to get out of the sand, they failed a drive check and damaged one of the 2 cars and slow it down. They made a drive check to get back and help the broken car, they made a throw check to lob some grenades and delay the demon dogs, and were making shots the whole time to try and kill or slow down the dogs. It was close but then at the end they made an extreme success to throw the last grenade to scatter the dogs, a good drive check to make it through the wadi, and they all made successes at STR or Dex to hold on as they were ALL in the 1 remaining good car. 

The one time I did it in Cyberpunk Red, Mad Max Raiders Vs Big Rig, I used a really big battlemat on Roll20 and did it tactically. With the PCs packing a bunch of MILITECH missile launchers, the chase didn't last long. Only one or two Raiders staggered off the battlefield.