For an easy going enjoyable older movie, DC Cab. Its rated R, so send the kids to the other room, but Mr T, Gary Busey, Max Gail, and Bill Maher star

Sounds like a Richard Pryor swearfest, but it's got Checker cabs throughout, car chases, good guys becoming a team and facing the bad guys, solving a kidnapping, and overcoming adversity.

Before the big boxy taxi, Checker made the Model A, here is a photo with a 1940 example

Via Shorpy. There are two in the photo, click on it for the full size, one is right behind the unbrella holder. Notice the antique 2 bulb stop light as well.

Hot Rod Checker Marathon Taxi... that is cool!

For more on this Checker, see Tere's photo gallery: http://justacargal.blogspot.com/2009/04/good-guys-reflections-omg-marathon.html