There are two types of players who can refuse minor league assignments. The first, and more prominent, are the 5 year veterans. Any player who has accrued 5 years of Major League service has earned the right to refuse any minor league assignment. If such a player exercises this right, his team must either reinstate the player to the active roster or grant him his unconditional release. If the player is released, the team is on the hook for the remainder of the player's contract. In this situation, the player essentially holds all the cards. Jason Bay (7.154 years of ML service, as of 6/13/11), Angel Pagan (5.046 years), and RA Dickey (5.081 years) are examples of this type of player.
The other type of player who can refuse a minor league assignment is a player who has either accrued at least 3 years of Major League service time (but less than 5) and/or has already been outrighted once in his career. This type of player cannot refuse an optional assignment, but he can refuse an outright assignment. In other words, if a player who fits these criteria is optioned, he has no say in the matter. But if he is DFA'd and sent outright to the minors, he has the right to refuse the assignment. If he exercises this right, he becomes a free agent, however he forfeits the remainder of his contract. If, on the other hand, he accepts the outright assignment, he automatically defers his right to become a minor league free agent until the end of the season, provided he isn't back on the 40-man roster at that time. Mike Pelfrey (4.024 years), Nick Evans (prior outright) and Jason Pridie (prior outright) are examples of this type of player.