Zaphod is put in the room where he will be killed by psychological overwhelmingness by being shown his significance in comparison to the entire rest of everything in the universe... and lives. Albeit, because he's actually in an alternate dimension where he is the most important thing in the universe.
Specific to the novels
Life, the Universe, and Everything
Our loser hero Arthur Dent escapes certain death by learning to fly.
Also keep in mind they are on a flying party at the time. Meaning Arthur just got Thor to throw himself into thin air. Seriously, that part is so subtle, it's easily missable and awesome in and of itself.
Another Arthur example. Summing it up wouldn't do it justice, but realize that the robot mentioned in the following paragraph has xenophobia, homicide, and world-ending destruction programmed into its mind and has proven throughout the novel that it is more than equipped to act on said programming...
He hurtled towards the astounded robot from behind. It still had its multifunctional battleclub raised...
With a sudden mad outburst of strength, he [Arthur] wrestled the battleclub from the startled robot, executing a dazzling banking turn in the air, hurtled back in a furious power drive and with one crazy swing knocked the robot's head from the robot's shoulders.
So Long, and Thanks for All the Fish
The prologue, a Call Back to the prologue of the first book:
And then, one Thursday, nearly two thousand years after one man had been nailed to a tree for saying how great it would be to be nice to people for a change, one girl sitting on her own in a small cafe in Rickmansworth suddenly realized what it was that had been going wrong all this time, and she finally knew how the world could be made a good and happy place. This time it was right, it would work, and no one would have to get nailed to anything.
Sadly, however, before she could get to a phone to tell anyone about it, a terribly stupid catastrophe occurred, and the idea was lost forever.
This is her story.
Ford bluffing his way past a crapload of armed security officers to smuggle himself, Arthur and Fenchurch onto a very public spacecraft.
Ford breaking out of the Guide building with everyone trying to catch him and still finding time to rip off the entire place. (It's under new management.)
Coupled with the Running Gag of him finding new and inventive ways to bankrupt the company using a stolen credit card. In one instance, he dials the Speaking Clock from a distant galaxy, collect, and then forwards the charges to the Guide.
Specific to the film
Slartibartfast showing Arthur the "factory floor" and Earth 2.0. Arthur is unsurprisingly floored.