Rereading the Prisoner of Azkaban, this interesting question(at least to me) popped in my head. What shape would a boggart take if a person is never depressed about anything, has no evil memories whatsoever for the boggart to feed on or has no fear?
In-canon, no-one knows.
A Boggart is a shape-shifting creature that will assume the form of whatever most frightens the person who encounters it. Nobody knows what a Boggart looks like if nobody is there to see it, although it continues to exist, usually giving evidence of its presence by rattling, shaking or scratching the object in which it is hiding. Boggarts particularly like confined spaces, but may also be found lurking in woods and around shadowy corners.
It's not even apparent whether a boggart actually has a physical form, but rather manifests as a force of nature:
Like a poltergeist, a Boggart is not and never has been truly alive. It is one of the strange non-beings that populate the magical world, for which there is no equivalent in the Muggle realm. Boggarts can be made to disappear, but more Boggarts will inevitably arise to take their place. Like poltergeists and the more sinister Dementors, they seem to be generated and sustained by human emotions.
Out of universe, there are very few people that lack a fear response and even those individuals (extreme psychopaths, sufferers of Urbach-Wiethe) do have a psychological (but not physiological) ability to identify things that they dislike highly, even if they lack the mental capacity to actually feel a fear response.
It's possible that they would have the same response as a Muggle:
The more generally fearful a person is, the more susceptible they will be to Boggarts. Muggles, too, feel their presence and may even glimpse them, although they seem less capable of seeing them plainly and are usually easily convinced that the Boggart was a figment of their imagination.
Perhaps it wouldn't turn into anything. From "Harry Potter and the Prisoner of Azkaban":
So the boggart sitting in the darkness within has not yet assumed a form. He does not yet know what will frighten the person on the other side of the door. Nobody knows what a boggart looks like when he is alone, but when I let him out, he will immediately become whatever each of us most fears.
It is safe to assume then if one did not fear anything the boggart would not change at all. You would know what a boggart's true form looks like.
Another idea is that the boggart would just guess what to turn in to, because as Hermione says:
It can take the shape of whatever it thinks will frighten us most.
This wouldn't scare the person of course but it might be rather funny...
They appear to have no form... Therefore, if there is no fear for them to transform into they will probably not even materialize or attempt to. Like dementors, they appear to feed off of emotions, so if there isn't something for them to feed off of, they will either leave or stay hidden.
When children learn to bear with Bogarts they make them change to funny things, so it's feasible to supose that a Bogart facing a totally fearless character (suposing that's possible) will probably switch to any form he can get from their "victim's" mind and it can be related someway to fear.
It would randomly switch between anything.
When Molly Weasley was trying to get rid of the Boggart at Grimmauld Place, the Boggart switched between her worst fears.
‘R–r–riddikulus!’ Mrs Weasley sobbed, pointing her shaking wand at Ron’s body. Crack. Ron’s body turned into Bill’s, spread-eagled on his back, his eyes wide open and empty. Mrs Weasley sobbed harder than ever. ‘R–riddikulus!’ she sobbed again. Crack. Mr Weasley’s body replaced Bill’s, his glasses askew, a trickle of blood running down his face. ‘No!’ Mrs Weasley moaned. ‘No ... riddikulus! Riddikulus! RIDDIKULUS!’ Crack. Dead twins. Crack. Dead Percy. Crack. Dead Harry ...
If a person didn't have a fear, their "worst" fear would tie between everything, therefore it would randomly switch between anything.