Jobs can tell us a lot about a person, but the fact is that very few jobs really showcase our true colours. Some of us will be lucky enough to snag that legendary "dream job," but most of us work because we have to, and that can mean anything from slapping a grin on our face when dealing with a customer we secretly wish we could disembowel with a teaspoon (and who probably feels the same way), to accepting a job well below our ability level because we need to pay the rent.
Our hobbies, however, can say a lot more about what we like and what qualities/skills we possess; after all, they're totally voluntary, and we may even be prepared to spend a lot of money in order to do something we enjoy. This is echoed in the media, where the mention of a character's favorite pastimes can provide a shorthand for their personality.
The weird thing is, once this hobby is revealed, a character's social circle tends to disregard everything they previously knew (or supposed) about their friend. If the Girl Next Door is revealed to be a kickboxer at the weekends, her associates will instantly assume that she's only "pretending" to be a wholesome sweetheart and is actually an Action Girl. On the other hand, if the school bully is revealed to attend piano lessons three times a week, he can expect a sudden upturn in his romantic success, as the ladies decide that his unexpected musical talent proves that he's a sensitive soul at heart, and hides it beneath a thuggish exterior. Given enough time, Flanderization may ensue to the point that the pastime becomes the entire point of the character, and scenes with the character before their pastime was revealed may feel out of place.
If, on the other hand, the hobby is introduced as the same time a character is — for example, "Hey guys, meet Marie, we met at the sci-fi convention last week" — it's the viewer who knows what to expect in terms of personality. Sometimes this will be exploited in An Aesop about not jumping to conclusions, especially if the person whose hobby is being mentioned is a main character. If they're a one-shot or side character, however, don't expect too many surprises; writers seldom spend time on revealing the complexities of a minor character's psychology, and are usually quite happy to let the stereotype stand.
Occasionally, the hobby will provide a "punchline" for the character because it is completely at odds with their personality. This may lend them credibility, as in the case of the Nerd who's also a skateboarder, or be a bit of an Achilles' Heel, as with the Alpha Bitch with an astonishingly large collection of comic books.
In Real Life, a hobby's demographic encompasses all sorts of personality types...but the world of fiction normally prefers to keep things simple, so the stereotypes endure. However, works where the writers really did do the research — or where the pastime itself is an integral part of the story — will be much more sympathetic.
Also worth noting is the fact that the associations and connotations of both hobby and stereotype will vary from place to place. See the Analysis subpage for a detailed exploration of this.