I would never say that Nino Rota is the best movie composer that lived.
There are too many good ones : John Williams, Bernard Hermann, Danny Elfman, Lalo Schifrin, François de Roubaix, Vladimir Cosma, Michel Legrand, George Delerue, John Carpenter, John Barry…
for those that I know or remember, ignoring geniuses whose music I don’t put a name on.

If i had to say who’s the best I’d say Ennio Morricone, but if you ask me who’s my favourite, I’d have to say Nino Rota.

No other one has expressed melancholy like he did, and no other film maker as expressed memory and nostalgia like Fellini.
These two are linked together, and both are a reason for me to love the other one’s work.

Together, they collaborated on 15 movies.
A good example of their symbiosis is one of Federico Fellini’s masterpieces : Amarcord.

The music here is one very important element, that enhances the main character child’s memories.
The theme is arranged in many different fashions along the film – depending on the feeling of the scene,
wether it is joyful, or very intimate – that usually refer to styles that were popular in Italy during the 30s.
But not only. In a very original way, it sometimes interfers with the action.
We can hear the score recorded by the orchestra, accompanying the images like in any other movie,
when suddenly a character grabs a flute and joins it, questioning the reality of what goes on screen.
Indeed, these are souvenirs, they are sometimes closer to dreams or fantasies than reality,
and that is a very poetic way to illustrate it.
In a similar way, several characters sometimes address straight to the camera.

Below is an example of how Amarcord’s music breaks the traditionnal score rules.

I think I’ve seen that in a few other movie since, like in Kusturica’s “Black cat, white cat”
(Goran bregovic being a great composer I forgot to mention).
In Terry Gilliam’s “Brazil”, the music played on any radio, by the orchestra at the restaurant, etc, is that old standard that gave his name to the movie.
Oh, and Morricone again, what about “Once upon a time in the west”, when Bronson plays his harmonica, and the orchestra joins him for an epic piece.
but as far as I know, Amarcord remains the best example of that practice.