There would be no Fallout franchise without Mad Max: the post-apocalyptic series by George Miller is probably the biggest single influence the games have.
If you're familiar with both Mad Max and Fallout, you have probably already noticed some of the similarities. Fallout is full of references and easter eggs that nod to Mad Max, and it's very similar in spirit, too. ShoddyCast went ahead and detailed many of these shout-outs, and they include:
1. In Fallout 1, you can befriend a dog that used to belong to someone that sounds a hell of a lot like Max -- but you can only do it after equipping a leather jacket. A jacket that looks like the one Mel Gibson wears in Mad Max.
This leather jacket reappears in pretty much every Fallout game thereafter.
If you've only played the more modern games, then you're still probably familiar with this type of dog easter-egg. One of Fallout 3's most iconic shots is a homage to Mad Max...
...and both of these are a reference to a book called A Boy and His Dog, which includes a dog called Dogmeat. Fallout 3's dog is also called Dogmeat!
2. In Fallout 2, you come across a location called Broken Hills:
It's a town that survives thanks to mining done by super mutants. One of the Mad Max movies was primarily filmed in Broken Hill, NSW.
Relatedly, Fallout New Vegas has an achievement called You Run Barter Town, which you get for selling 10k caps worth of stuff. Bartertown is also a location in Mad Max.
3. In Fallout 3, you meet a character that mispronounces "humongous" as "humungus." Humungus is actually a Mad Max villain:
Humungus happens to have a gun that looks a hell of a lot like the scoped .44 magnum in Fallout games. But that's not the only weapon that Fallout seems to ape. The sawed-off shotgun in Fallout: New Vegas looks a lot like the shotgun that Max wields in the movies:
4. This one is my personal inclusion. You can meet a character named Mel in Fallout 3. He carries a sawed-off shotgun that isn't loaded, which is a clear reference to Max's unloaded shotgun in the movies:
You can also meet a Mel in Fallout 2.
ShoddyCast goes into more detail for most of these references, and even talks about some of the thematic similarities between Mad Max and Fallout -- so you should definitely give it a watch if you can.