If you ask me, I do think that life of a teenager, these days, can be quite difficult. First of all it's the time when they need to start thinking about their future and decide what they will do with life and most of the teenagers are not sure as to what life holds for them. What University they will get in and what will be the career that they will be making is uncertain. It puts a lot of pressure on them and people around (their family, teachers) having high expectations of them doesn't help to reduce the stress at all. If they don't get into university or fail an exam or get a bad mark at school, everybody makes it sound like the end of the world.
Another very hard thing for a teenager are relationships at school with peers and at home with family members. Let's be honest, teenagers can be cruel. Going through the bullying at school can be seriously traumatic. Even if it not bullying, sometimes peer pressure forcing you to conform to standards and hobbies of the majority. There's often the fear of being misunderstood, misjudged or rejected. It makes them hide the real selves and be the way peers want them be.
Relationships at home can be as hard sometimes, because parents try to control teenagers a lot. Better part of the parents don't see their kids as a whole person, with a developed personality, who can decide for themselves and make their own mistakes.
You get told to act like an adult but you still tend to get treated like a kid. 
Also teenagers go through some changes in their body. They become very conscious of the way they look. They have mood swings all the time, can be angry without a cause a lot.
As for things that teenagers value I think those are privacy and independence. Also close friends. The family that is always here for them, that cares about them, loves and supports no matter what.
Those are pretty simple things, but I think they are what can make every teenager happy.