Holden is the main character as well as the narrator, so this is a pretty easy role to assign. Some have suggested that Holden is an anti-hero – he lacks the noble characteristics that most heroes have, characteristics like honesty (Holden is a perpetual liar), courage (he admits to being yellow), strength (he says he's a pretty weak guy), and decisiveness (Holden is plagued by passive inaction). So, sure, in this respect, Holden is indeed an anti-hero. He isn't particularly good-looking, creative, or funny. He irritates people all the time. He worries his parents. He mopes around.
But, Holden is also one of literature's favorite characters, and clearly, this is for a good reason. Look at Holden's nobility, at his unceasing desire to protect his family, Jane, and children everywhere. Look at the compassion he expresses in the way he views Sunny (as a person, not a prostitute) and the nuns (who he recognizes never get to go to swanky lunches). Not to mention, his one life ambition – to be the catcher in the rye – is one of the most heroic (if implausible) goals we've ever heard.