I've got a teenager. The sort of things I buy her are things she cannot generally afford like expensive perfume, clothes & jewellery. These things are very dependant on the individuals personal taste. Like I've been given some shockingly horrible jewellery by people like my m-i-l which was obviously an attempt to get something she thought I liked. My basic rule of thumb with anything is to buy the genuine article ie if you can't afford gold, don't get something gold plated, get something funky made of wood or whatever.
If I get cheaper gifts for my daughter, I try to buy her something of good quality that is ethical so I can kinda show them the way
Quite a few examples of things I have brought her are :
I got an awesome duvet cover & matching pillow slips from the fair trade shop in town the other day. It's dark navy blue with these cool batik spirals all over it. A couple of organic cotton towels & some enviromentally friendly washing powder. A few bars of organic fair traded choccie. I agree you can't go wrong with music vouchers. Decent hair care products ( eg Paul Mitchell ) can also be a good plan. Body piercing jewellery can be good if they have piercings. The hippy look is very trendy at the moment so a nice crocheted hemp bag or a bag made from the top of a pair of levis or something like that could be another idea. An essential oil burner, a few candles for it & some nice oils. dd loves journals so I try to get her ones that are different. I got her one made of recycled paper with the cover made of dried leaves but with moon & stars pattern the other day. Cruelty free black eyeliner & mascara. Funky cushions to go on their bed. Bath bombs which you could make yourself. A decent recipe book. A coffee plunger & manual cappachino milk frother & some fair traded coffee. Some herb tea. A basket of fruit. Some fair traded organic hot chocolate. Cruelty free lip gloss. I got her a big ball of labradorite one year she really loved. Lava lamp.
As for clothes. You should be able to tell by what they wear. A pair of levis is always a good idea. Plus if they already wear them, just read the label at the back for the size & style# If not, make sure they're low waisted or even hipsters. A nice type of hippy top. Some surf brands you can't go wrong with either. Mambo, Billabong, Aztec Rose for example do some really cool women's clothes. They're more expensive than your standard teenage shops but are far better quality & look far better on.
Final safety net, always get an exchange voucher just in case.