In the movie, when Harry and Ron are being surrounded by the Acromantulas in the Forbidden Forest, the car out of nowhere comes to their rescue. Why does the car do this?
Unfortunately I haven't read the book in years and my google foo seems to be failing me.
The car appears to have spent quite some time driving around the estate after having ditched Harry and Ron (following the unfortunate incident with the Whomping Willow). When it detects that they're in trouble, it comes to their aid. Note that the car has an easy familiarity with the path in and out of the forest.
Since the car belongs to Ron's father (and may or may not contain parts from Sirius Black's motorbike), it's hardly surprising that it would rescue them when the need arose.
Mr Weasley’s car was thundering down the slope, headlamps glaring, its horn screeching, knocking spiders aside; several were thrown onto their backs, their endless legs waving in the air. The car screeched to a halt in front of Harry and Ron and the doors flew open. ‘Get Fang!’ Harry yelled, diving into the front seat; Ron seized the boarhound round the middle and threw him, yelping, into the back of the car. The doors slammed shut. Ron didn’t touch the accelerator but the car didn’t need him; the engine roared and they were off, hitting more spiders.
They sped up the slope, out of the hollow, and they were soon crashing through the Forest, branches whipping the windows as the car wound its way cleverly through the widest gaps, following a path it obviously knew.
Chamber of Secrets - Chapter 16
As to why JKR chose to have them rescued by the car (e.g. as opposed to a different deus ex machina), it's because she personally associates that make of car with a joyous sense of freedom:
The Flying Ford Anglia was based on a real car driven by Séan Harris, the first of my friends to learn to drive. We were at school together. At the time I lived in the middle of nowhere and had to rely on my parents for transport. Sometimes Séan would come for me in his car. The sight of that car meant freedom to me…my heart still leaps whenever I see a Ford Anglia! That’s why , when I thought of Ron’s flying car, I immediately pictured a Ford Anglia. Renton, Jennie. "Wild about Harry." Candis Magazine November, 2001
In Harry Potter the Chamber of Secrets there is the car its in a little scene that they deleted and also you can hear it roar faintly in the background and if you brighten up the screen you can see the car in the corner of the screen in the movie version there's also the bonus disc version of the two-part two-disc series of Chamber of Secrets and all the additional scenes that where cut in the movie that you could go into and see once you go into the menu of the second disc.
That's why the Ford Anglia in Harry Potter and the Chamber of Secrets came and saved Harry and Ron from the spiders because they saw the car and that additional scene and the car some how saw their footprints in the mud when they walked and heard them screaming and the dog barking that's how it found them and save them.
