It's probably not completely surprising that the two of them don't interact all that much (it wouldn't make much sense for them to keep running into each other all movie long), but the first time they really square off, it ends with one of the most breathtaking shots of the 90's.
"He Just Did a Peter Pan Right Off This Dam..."
He's got to be, right? I mean, who steals an ambulance as a getaway car - and then turns on the siren, as if all that stealth was getting on his nerves. Luckily for him, the tunnel he's trapped in has large drainage pipes...also, the tunnel he parked in is a dam.
Deputy Gerard, being of sound mind, figures out that Kimble is hiding in these drainage pipes, and doggedly follows him down. He clumsily slips and drops his gun, which finds its way into Kimble's hands. Kimble takes the gun and steadfastly maintains that he didn't kill his wife. Deputy Gerard's reply is classic.
"I don't care".
Kimble wasn't ready to hear that. With a sort of startled look, he turns tail and runs. Gerard grabs his second gun and follows him. He finds him shortly thereafter trapped at the end of the drainage pipe, which - again - is a dam.
With no options left, Kimble jumps.
The shot of him falling through the air to the churning water below always was awe-inspiring to my brother and I. Sometimes we'd rewind and watch it twice. The part that always catches me now is how Tommy Lee Jones plays the whole thing. From "I don't care" to "He just did a Peter Pan right off this dam..." the whole scene is great.
Watch the whole thing, annoyingly split into two parts, because I couldn't find one with the full thing.