If you buy a pre-owned game for your Vita, you'll get a warning that only the first player to use the application can earn trophies in it. Whether to prevent players from earning trophies based on other users' saves or to discourage the used game market, Sony has decreed that only the first PSN account associated with a game card can reap the full rewards of playing through it.
Fortunately, this is simple to circumvent — all you need to do is format the pre-owned card. Pocket Gamer has outlined the steps to erasing the data, which basically consist of touching and holding the screen as you would if you wanted to rearrange the icons, then hitting the "…" bubble at the top right of the game's icon and selecting "Delete." The previous player will keep his or her trophies, but the card will be as good as new, with no saved games or associated PSN accounts. Presumably, this could also be done before selling a game if you want to keep those Uncharted saves all to yourself.