The goal-keeper is most at risk for running into a post, or getting kicked in the head. I've seen both. I support any keeper who wants to protect his/her head.
Our daughter plays and we worry about her as she gets older and the game gets more physical. We would never allow her to play goal--too dangerous. Outside of goal, the main risk is ACL injury. In addition to high-speed headers, there are plenty of elbows to the head as well as the dreaded head-to-head collision. Head-gear? By all means.
The other thing I've seen from time to time is that sometimes you'll get leagues who have one-size-fits-all goalposts to try accomodating all ages, where the goalposts split the difference between youth and adult players, which causes the goal to be too small for older players. For players 12 and up, the goal really should be FIFA standard-regulation 8 feet high by 24 feet wide - anything less is just asking for trouble.