Jarmusch is often consigned to the critically lazy category "acquired taste". His films are usually slow-paced, seemingly directionless, often focusing on dead-beats, outsiders, foreigners and other socially marginalized figures. As he's said himself, if he see's a character taking a phonecall and arranging a meeting, a cut, then the meeting itself, he wonders what the character might have done in the interim to amuse himself. Was he bored? Nervous? Did he watch some tv? Sing along in scat to a crackly jazz record on the radio?
If these kind of questions interest you, most likely Jarmusch will. 'Down By Law' is a visual treat, a fact quickly prefaced by its opening shots of New Orleans, seemlessly concluded with the final, symmetrical frame of the protagonists going their separate ways. If the performances are very natural but also very idiosyncratic, that might be because John Lurie and Tom Waits are principally musicians, not actors. And because Roberto Benigni genuinely knew very little English when the film was made.
The music, and the story, are enchanting, surprising and resistant to full narrative closure or an obvious moral. Benigni was not then the worldwide star he is today, and he has to fight on screen for air-time. It's worth the wait when the master comic raconteur gets going.
So here are some tips:
(1) if you like Benigni in this, check out a later Jarmusch film 'Night on Earth'. He gets a full half-hour solo as a chattering taxi driver. More adult than 'La Vita e Bella'. Funnier too.
(2) if you like John Lurie and Tom Waits, listen to their music. Between them they've scored a subtantial amount of Jarmusch's oeuvre. Lurie also stars in 'Stranger Than Paradise', an earlier Jarmusch film.
(3) if you like the style and pace of Jarmusch, dig a little deeper and watch some of the filmmakers who influenced him. John Cassavetes and Yasujiro Ozu I'd particularly recommend.
(4) if you wonder "who is Jim Jarmusch?", watch Wayne Wang and Paul Auster's 'Blue in the Face'. You'll get a good 5-10 minute cameo riff from the man himself on the merits of smoking.
But 'Down By Law' is a great place to start. It's a top dollar showing from Jarmusch's penniless down-and-outs.