Yes, include spoilers (behind spoilertags if you want).
Spoilers may be necessary in order to correctly identify a story: a particular kind of twist ending might be a story's most distinguishing characteristic. (For example, take Neil Gaiman's American Gods: various elements of the story are similar to Joanne Harris's Runemarks or Rick Riordan's Percy Jackson series, but the ending is enough to distinguish it from these, so that's what we'd want to see in a story-ID question about it in order to narrow down the list of possibilities.)
Also, anyone who's able to answer a story-ID question will likely have read/seen the work in question, so they won't care about spoilers. As for other people reading the Q&A: if they already know the work, see above; if they don't, they won't recognise it anyway and so won't be spoiled much by a full description of it. So I'm not even sure how useful spoilertags would be. Probably mainly for people who are actually in the middle of the story, so they know how it starts but not how it ends - or perhaps people who get reading/watching recommendations from interesting-sounding ID questions on SE.