Unless you're against AA or KK the worst situation you'll be in is a coin-flip. With the money already in the pot, the pot odds
generally support the call. However, in a tournament that can be the end of the tournament if you lose the flip. The variance of calling the all-in is liable to be huge, because you're often getting only marginal odds in favour of calling. Your read on the opponent is important, though - if they'd only do that with a high pocket pair, then you may want to lay it down, but if they'd do that with AQ or AJ or KQ then you generally want to take that all-in bet because there's a fair chance that you'll be the favourite.
Against 1 or 2 players you probably want to put in a continuation bet most of the time - more often than not the flop will have missed your opponent as well, and you will often pick up the pot there. The other reason to continuation bet when you miss is that this disguises the hands which hit, so that when you bet a flop you like, you'll get paid off much more often.