Best chase movies

Blues Brothers by far my favorite.
Would have to mention Blues Brothers 2000. The story sucked, but it was certainly another chase film. By the way although the story sucked in BB2K, it’s worth watching just for the music.
I loved that last scene when they had all those great blues masters jamming it out. Belushi was sorely missed.

Breakdown with Kurt Russell
second for Midnight Run

The French Connection, which also has one of the best car chases ever put on film.

Not to mention its quasi-sequel, the Seven Ups.

By the (banned) OP’s definition, I’d say virtually any detective movie fits the criteria.

Slither, with James Caan, Peter Boyle and Sally Kellerman. The main chase vehicle is a black-ops, stealth-looking Winnebago.

Harold Lloyd’s Speedy (1928). Harold is hauling ass through old New York in an ancient horse drawn streetcar. One of the highlights is, when filming, the streetcar runs into a bridge support. They manage to work it into the movie. The film also has great scenes of '20s Coney Island.
In *Girl Shy *(1924), Harold races across town to stop his dream girl from marrying an already married man. In both films, the obstacles thrown in his way, and how he deals with them, are pretty inventive (and funny).

CAN YOU DIG IT!!!
I would suggest
Predator
Public Enemies
Natural Born Killers
Tears of the SunTankwith James Garner
Crank

A few more; not necessarily contending for best but worthy of discussion:

Buster Keaton’s The General, probably the most glaring omission so far

Sugarland Express. Spielberg’s first theatrical film

The Gauntlet, '80s Eastwood vehicle

Blade Runner

Von Ryan’s Express; more trains chasing each other, woo hoo!

Kudos to those who have mentioned rarities such as Slither and Speedy.

So Bo, it’s been 6 years - have you seen District B13 yet?

They have it free on Netflix - that how I saw it.

It’s absolutely silly, but very fun.

I really liked Go, and I think that it would qualify for the category, even if it wasn’t all one big chase like some of the other movies mentioned.

I thought it was one of the better films around that features the same story told by multiple perspectives…

I don’t really think of it as a chase movie, but it is just all kinds of awesome.

Virtuosity Fun movie and you get to see both Denzel Washington and Russell Crow naked (or close enough)

+1, great chase. And we never find out what it is they’re after! A case? “What’s in the case?” “I don’t remember.”

Run Lola Run (1998)

My all-time personal favorite: Keaton’s Seven Chances (1925). Up there with The General, mentioned previously.

Okay, it’s just one scene, but the car chase scene in Bullitt is freaking awesome: