There are different situation for games having multiple endings. For instance, a game that may have multiple characters, leading it to have multiple story lines for each of the character. That results a game having multiple endings, which in fact just means having multiple linear stories within a common time frame. Although it can easily evolve to be the story line between each characters affecting the others', resulting each of them will be having more than one ending.
Another situation for game to have multiple ending that I can think of is, even a single story line sometimes would have multiple endings. Secret boss and hidden scenario = secret ending, are very commonly seen. I personally think all these multiple endings approaches would give a game another depth and made some of them so unforgettable (e.g Chrono Trigger
).