A word for someone who does not keep up with popular culture

Anyway, some wild guesses following the question title, might be:

unfashionable, unstylish

or maybe reserved, discrete, if you mean someone introvert

Some of these are spoken slang:

• square
• daggy (http://www.urbandictionary.com/define.php?term=Daggy)
• uncool
• untrendy
• out of fashion/style/trend/ (That just proves once more that he is so out of style. He needs to get with the age. Even Ashanti isn't in, anymore.)
• old-fashioned
• not in fashion (Pink is so not in fashion! DUH! / Why are you wearing white shoes, they are so not in fashion.)
• not in (She is so not in. / Even Ashanti isn't in, anymore.)

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Edit:

I'm sorry, I've only now realized you're not looking for a judgmental term, but for something complimentary. Someone's already come up with "fad-proof", and that gave me this idea:

• fad-free

I construe it as a pun on fat-free. It might perhaps still be seen as derogatory, but this time not as directed toward you, but rather extending from you. There's a blog with that word:

100percentfadfree

According to the mass media, the current fads are all about being half-naked... but you don't have to sell your soul to be fashionable and look cute! Don't let anyone tell you that modesty is boring... or ugly, frumpy, dumpy, drab, or dull. Modesty is all about beauty. It is classic, timeless, and fad-free.

While something could certainly be constructed that would make sense to mean what you want, I think it's important to keep in mind the context of when such a phrase would be used. It sounds like you want something to use in everyday social conversation, which means that the answer must not only work but already be in common usage. I like "non-ephemeralist" from the comments, but it's not something that people actually say, so you'd have to follow it up by explaining what you mean in a lengthier form anyway.

I don't think there really is a specific word that fits. I might say something like "I don't follow pop culture," but that's probably overly broad - I do, for instance, follow the worlds of music and video games, which are certainly part of pop culture. You'd have to be more specific - "I don't follow celebrity gossip." Or, as a sort of metonymy, "I don't read tabloids."

I would call them an individualist, free-thinkers, or someone who marches to the beat of their own drum. They are not shackled by the pop culture dogma that surrounds us in everyday life, which is constantly trying to tell us what we should be liking or is worth spending our time, energy, or money on. They may occasionally like the same things that are considered pop culture, but it is purely because their tastes happen to coincide and not because they actually follow trends or the mainstream ideas of what is "in".

They are people who have grasped the best of their own freedom to like whatever they want and lack the concern for other people's opinions that often drives us to watch, listen, or buy just because everyone else is. They are often the innovators who come up with new ideas because they are venturing into ideas or passions different from what is popular now. They are the ones who will start tomorrow's trends.