If you didn't read to your teens as kids, starting now might be awkward, but both my kids still love it when I read to them. In fact, The Boy is pretty exclusively an audiobook reader. He had such a hard start in school with constantly changing/bad reading curriculum, I love anything that gets him excited about books. We listen together in the car too.
Reading the same book together is a great way to share reading if you didn't read aloud as a kid, or if your kids have grown out of the activity. My daughter is only home at school breaks, so it's a great way for us to keep in touch -- like a book club of two. And she usually recommends the books.
I hate the phrase "teachable moment" because I feel like puts way to much pressure on parents and takes away from that amazing feeling you get when you can actually talk to your teens in an adult-ish way about your feelings and beliefs.
But books really open up those kind of fun conversations in our house, and I'm a firm believer in giving kids as much of a chance as possible to form their opinions in a safe space so they understand how to stand up for themselves and others as civilly as possible. I don't understand shutting kids off from other viewpoints; the more kids hear their parents offering defense of their own beliefs, the stronger they become and the more able kids are to form their own strong opinions.
Here are some great titles if you're looking for a place to start*:
Freak the Mighty
Chances are, and especially with bullying being such a problem in schools, your kids are reading Freak the Mighty in school. The movie is good too, as is a similar bit of 80s awesomeness My Bodyguard (Firefly/Chuck fans, you can see where this mom started crushing on Adam Baldwin -- scroll down for trailer filled with all your favorites 30 years younger).
House of the Scorpion
Cloning, genetics, personal freedom, immigration, drugs, utopian/dystopian societies -- this book deals with it all plus excellent story and characters. This was a recommendation from The Girl, our whole family loved it, and I've recommended it to teens and adults. This month in book club we're reading The Adoration of Jenna Fox, which deals with similar issues of cloning and personal freedom versus government control, but the scope is much smaller.
The Bloody Jack series
I was afraid my son would not be interested in Bloody Jack, but he took to it more than I did, which I love because equality issues can be explored without anything heavy handed. A teenaged Mary decides her life as an orphan on the streets of 1790s England would be much improved if she changes her name to Jack and poses as a shipsboy. Author L.A. Meyer handles the mechanics of hiding gender realistically but not graphically, especially heartbreaking when -- and moms will see this coming as she starts getting regular meals and starts putting on weight -- Jacky, as she is called, gets her period and thinks she's dying, but can't go to the ship's doctor without revealing her secret. Even though my son watched The Movie in sixth grade, I did have to tell him what was going on.
Hold Me Closer, Necromancer
I admit I picked this one up because the title made me laugh, and all the chapters are similarly based on song names, so that will appeal to other moms my age, give or take. The story is mostly very fun, and a cut above the usual monster stuff that shelves are overrun with right now, and it has a lot to say about friendship, which is always important.
*Your kids are likely reading Hunger Games in school, and since my daughter didn't like this series, I didn't read it until recently when we did it for teen book club. I didn't like it either, but I know I'm in the minority, and there is definitely a lot to talk about in it. My son liked it though, and I find it's similar to a lot of the books/series he likes: it involves levels like a video game. I feel like it's basically the same thing happening over and over with detail variations. And, as a parent, I couldn't get past the basic premise that a central government would be able to come and get people children for 70 years and there wouldn't have been a major revolt, like, immediately. There was something inherently false about the Lord of the Flies atmosphere. Of course, I felt that about Lord of the Flies too.