Yes, you'll be able to continue collecting digital trophies when you move your PlayStation Network account to PS4. All your trophies from PS3 and Vita will remain intact, and you'll be able to browse through them even on Sony's next-gen console. PS4 adds one new feature to the trophy-collection mix, however: you can see how rare they are.
In a separate column next to when you unlock the trophy, you'll see the percentage of players on PSN that have been able to unlock a trophy. This should be helpful for developers too, when they discover that only 0.1% of you ever unlocked their seemingly-easy Bronze trophy.