Almost any time people make lists of suggestions for aspiring writers, one of the bullet points is "avoid current slang, pop culture, or technology. This will make your book seem dated in five years."
This much is true: if you're using slang and "modern" references in attempt to connect your book with "today's teens and tweens" (or using the phrase "today's teens and tweens" at all), you're picking the wrong way to get readers to connect with your book.
But as long as a writer understands this, I think that leaving pop culture out altogether is fairly bad advice. If your main character is a teenager, then slang, pop culture and technology is probably a big part of their life and will probably heavily influence the way they see themselves and the world. Characters in historical fiction have no problem using the slang of their day and dealing with current events - why shouldn't modern characters? And, most importantly, you need to know that leaving that stuff out won't protect your book against being dated in five years one little bit.
Making up your own slang and pop culture (as I usually do) might buy you a couple more years, but slang isn't the only thing that's going to go out of date in five years. I originally planned to make this post into a list of things I took for granted as a teenager that are out of date now (or about to be): things like licking stamps, getting chicken pox, seeing people smoking at the mall, scouring used book stores for a book I can't find a copy of anywhere, renting a video at a video store, buying film for a camera, missing a TV show and being unable to see it the next day, watching TV for hours trying to see a certain video or commercial, or having my parents have no way of getting in touch with me when I'm not at home... but the list was just too long in the end.
There's no way we can predict which slang terms will last, or which facts of life of today will soon go the way of the milk man, "going steady," and worrying about getting drafted during peacetime. Even more importantly, we can't imagine what sort of things will be facts of life for people in 10 years. Having instant access to nearly every piece of music ever recorded, reading a book on your phone, and pushing a button on your phone to identify a song playing on the radio would have seemed like science fiction when I was a kid. It's all totally normal now.
So I say to go ahead and use slang and pop culture if you feel like it. Just remember: this stuff is a part of your characters' lives, not the way to make them seem relevant to your readers. As long as you know that it won't make readers connect to your book automatically, even on the day it's printed, using "modern" references can keep you in mind of the fact that the world of your book will seem dated one day, and force you to focus on the important stuff that will help it stand up for readers who have never licked a stamp, made a "long distance call," or met a person who didn't have a chip implanted in their to download news and the weather to their brain every morning.
Interesting characters will stay interesting for years - maybe for centuries if you play your cards right and get lucky. Engaging, surprising plots should still hold a reader's interest for years to come (there are plenty of still-great books out there with plots that couldn't happen in a world with cell phones). It's all about the stuff that WILL last: loss, longing, heartache, identity, growth, disillusionment, hope, fear, love. Pop culture can shape your characters - it shapes every generation. But it's how your characters deal with growing up and with the world around them that will make your book stand up long after it becomes a period piece. Make your characters humans, not just blank slates that will seem equally blank in ten years.