I've played a lot of refusal chess over the years. Back when I used to be active in local chess clubs, it would invariably sweep through the club for a while (like bughouse, another great variant).

First of all, if you have only one legal move, your opponent CAN refuse it, in which case you lose. However, that is offset by the fact that the previous move that put you in that predicament, might itself have been one you could have refused. Also, it IS common to "bluff" about half of the time, by playing your second-best move first in the hopes it will get refused.

The game ends up very interesting, as "looking ahead" requires you to, in effect, consider the consequences of each player's second-best move. Counter-intuitively, this can lead to very lively positions, since both players can leave a piece unguarded (the capture would just be refused)... but if you have a piece unguarded, you don't have the luxury of refusing other moves. Sometimes the resulting positions can look very odd, and tricky to calculate.

It's also great for speed chess - to refuse you just punch the clock.