Is it possible to ask for a story identification where the story itself isn't really sci-fi or fantasy related? For example, a story like a memoir or fiction about old England... or let's say somebody asks a question and it turns out the answer is "Saving Private Ryan" (not sci-fi or fantasy in genre, but nonetheless a story).
If not, which SE site should I go then? because I have a genuine story that I've read a long time ago but already forgot about the title and only remember parts of it.
If it's not a Sci-Fi or Fantasy work, it's not on topic here and will be closed.
If the description doesn't seem to have SFF-like details, the community is pretty good about closing the questions and asking for clarification on what parts make it SFF (if any). If there are none, it'll stay closed.
The Literature Stack Exchange is now public and seems to currently allow story identification questions from all genres. Rand's answer addresses this, but visiting Literature meta is the best place for advice on their scope and guidelines.
As CreationEdge says, please don't ask here if it's not sci-fi or fantasy.
Instead, you can ask on Literature SE, a relatively new site which is currently in public beta. That site has already had several story-ID questions, none of which so far have been closed or have a negative score. The conclusion of the corresponding meta discussion seems to be that they should be allowed until/unless they become a problem (e.g. the site starts getting overrun with low-quality ID questions).
So if you have an ID question about a written work which isn't sci-fi or fantasy, Literature may take it. However, as always, please do try to make it as thorough as possible, and include every last detail you can remember of the story. Please check through the answers to How to ask a good story-ID question? here on SFF, to see if anything on those checklists jogs your memory for more detail.
Playing Devil's Advocate, if it's ambiguously SF&F, it might do alright. I've had a few ID questions like that, where I could not remember whether there were actually fantasy elements to the story, or if people just thought that they were in-story. For example, Children's book about a girl maybe being influenced by her black cat to become a witch and Teenage boy travels to Scotland to settle his family's curse. Alternately helped and hindered by a girl from the rival family. Smoked fish?. Although, admittedly, both were slightly ambiguous as to whether there was magic after all. I have a third question that I've never asked here (involving a pair of kids who are convinced that their next-door neighbor is a witch, and manage to convince her enough to play along and try to be one) because I'm 90% certain that it was clear by the end that there was no actual magic.
In cases where it has been found that the work in question is unambiguously not fantasy/sci-fi, I've voted to close, since the question is not on-topic, although it will often stay on the site, because some of the answers are fantasy/sci-fi, and could help others (to give a contrived example, imagine someone looking for a film where a girl keeps getting gifts from her "fairy godmother", they wind up accepting an answer that points out that it's a 1970s TV film where the "fairy godmother" is found to be their mother, secretly encouraging them, no magic involved, but there are also valid answers that match the original question but refer to actual fantastic works).
