Choices need to effect the storyline in some noteworthy way, or there's simply no point in having them there. Why even put my character in there if I can't roleplay as that character and make their decisions?
A story can still be made when you're railroaded through and can't make any of the decisions, but there needs to be few/none of the "Why don't you just do X?" moments. Something like "What do you mean we HAVE to keep the bitten ally in the party? Chuck the guy out before he zombifies! Grr, game y u no have choices?!" and you usually have your player character not be the main character in the story for it to work.
So having choices is important, but I'd still like to have the routes be relatively clear. Games like Fallout where there's so many paths you'll never see them all without a guide feel overwhelming.