There’s 1975’s diaster flick The Hindenburg with Anne Bancroft. That’s the only one I can think of offhand. Are there no other dramatizations of the Hindenburgh diaster (unlike the sinking of the Titanic)? German films? What about movies set her elder sister, the Graf Zeppelin (which flew around the world)? Or set on fictional passenger airships? Sky Captain and the World of Tommorow had zeppelins in the back ground (including docking at the Empire State Building), but but it wasn’t set on one.
One of the Indiana Jones movies has some film time on a zeppelin, but it’s not a majority of the film. Not sure if that counts for your purposes.
That would be Last Crusade.
I assume the OP is specifically requesting zeppelins and not just blimps (View to a Kill, Black Sunday)?
This (unseen by me) looks like it’d fit the bill…
As I recall, The Rocketeer had a climatic fight scene on an airship.
There’s the Michael York film Zeppelin about Germans trying to steal the Magna Carta with a Zeppelin during WWI. Or the even less serious film, Sky Bandits (a.k.a Gunbus).
Try here.
The first one that came to mind for me was “Up”.
Do blimps count? (I’ve never seen it, but I’m assuming there are at least some scenes aboard the blimp.)
Zeppelin vs. Pterodactyls, which, if it had ever been made, would have been the greatest effing film ever!
I so want to see that.
ETA: Though, as a Hammer film, it would probably be sadly dull and unfulfilling. 
The Assassination Bureau has a pretty impressive zeppelin-borne climax. Plus Diana Rigg in her prime. 
Black Sunday was a pretty decent thriller with a blimp used to detonate a massive bomb over the Superbowl.
The Song Remains the Same
(Well, somebody had to say it.)
Blimps are diet Zeppelins.
We will overlook your lack of classiness.
I remember The Assassination Bureau, I was so in love with Diana Rigg at the time.
The Disney film Island at the Top of the World has great airship.
In the Howard Hughes movie Hell’s Angels, there is a zeppelin raid on London during WWI.
It morphed into a film to be called **The Primevals, which they actually started filming, but sadly never finished:
http://www.animationtoolworks.com/examples/primeval.html
David Allen was doing it. I understand they made a short to try to sell the film. I don’t know if any existing footage has zeppelins in it. They did a special issue of Cinefantastique about this some thirty years ago.
I think there’s a Zeppelin in Kiki’s Delivery Service, and I expect there are quite a few more scattered through various other animes.
Zeppelin! (2005) is excellent, with great footage of the original Zeppelin works, etc.
Well, there’s always the gift-unwrapping scene from A Christmas Story.
The Fabulous World of Jules Verne features scenes on airships that are even cooler than Zeppelins (check about four minutes in).