Picture this, you unlock a Grand Theft Auto Trophy and along with it unlocks a custom avatar picture for your profile. You see a recent player that you played with has a Moogle emoticon from Final Fantasy in their profile that you want to unlock and use in your chats - thus starting you on a quest to play Final Fantasy. Accidental discovery is the theme, and it's important. The journey a player can be taken on is what they will cherish more than the reward.
This is one way of reinventing Trophies entirely. It's fun, it's organic, it will take a lot of work to maintain and it will be worth it. It will get people interested in browsing profiles and community pages, it rewards people for discovery and it allows for individuals to express themselves in unique and quirky ways. The weirder the profile, the better.
Ideas for rewards (1 reward per Trophy):
The reward for collecting every Trophy can be the best reward as determined by the developers. Along with this it would be nice if there was a unique tier of rewards for completing a game to 100%. For example a special badge could be granted that can directly go into a specific section of a players profile.
A separate set of rewards can be specifically developed by the console manufacturers for reaching certain meta objectives like 5, 15, 25, 50 complete games or reaching X game level.