Heh. Good point.

Coming from a 14-year-old guy, mentioning you like classical music is going to produce one of two results. A) "you like classical?!?!" and an immediate classification as "uncool", or B) a nod which indicates some form of respect, a "you're a better man than I am". A happens more often, which is why I don't mention I like classical until I've known that person awhile.
To answer the question, I do think it's relevant today. For the same reasons the Mona Lisa and Michelango's David are relevant.

You're talking with some right douchebags if mentioning classical music puts you in the uncool category. I figured your Beach Boys love would do that for you :p:.

I've learned not to discuss music with the right douchebags I know - that's why I'm here. My friends all respect my tastes, even if they don't get them. And as for the Beach Boys, no one in my generation has heard of them. Somewhat a good thing for me! They don't rate very high on today's cool-ometer.

It's best not to confuse how well something is appreciated with how relevant it is. We've been condition by the rigid and simplistic structure of contemporary music to the degree that we're not be able to effectively listen to classical music when it's presented to us, and for the most part that is why classical music creates a sense of boredom, or sometimes bewilderment when it hits our ears. Combine that with the general ADD nature of our culture and you have the reason why itis underappreciated as an art form.

Classical music, more so than any other style, conveys the full depth of the pathos of the human condition. It's been with us for over 1000 years. Compare that to jazz, which is roughly 125 years old, or rock which is about 60 years old, or hip hop which is a little over 30. Classical music is extraordinarily relevant, because it is emblematic of human catharsis and the true depth of human experience. Contemporary music might be more representative of the cultural zeitgeist, but I think classical music is more relevant in general.

I like classical music from time to time. Granted I could not listen to it all the time but from time to time it is good to relieve my stress.

This is essentially the equivalent of saying that if something is occurring in the world today that isn't covered on the evening news, then it has no impact on us.

No bloody way.
Even today classical music is of big relevance,
and it is a huge inspiration to get a free and light mind,
to be able to get through your day with a big smile.
That is what relevance is in my eyes.
Music that is able to inspire, that is able to make people smile,
that is able to make them angry, to make them think, or laugh..
THIS is relevance. You are talking about popularity,
and popularity is nothing, but a fading shadow.
At day you see it cleary - and then the sun sets,
and you can only see its echo, projected by electrical light.
Until even that is gone, and the shadow's "popularity" with it,
but not its relevance

I think people are forgetting that this is the question in the OP.

Is it relevant overall sure because of how it is used in other media outlets and it being the foundation of what is being produced today but the OP isn't asking about overall relevance.

It is asking about relevance as it pertains to today's music and the popularity of today's music.