The current policy is that it is up to the individual community. There is no network-wide ban on them currently. But they're a very dangerous question type, so it may be all the better to avoid them if possible.
To clarify Gaming's exact stance, identification questions are tentatively allowed under increased scrutiny. And I would suggest that if any other site wishes to entertain them, they'd do well to be very mindful in monitoring them as well.
You can think of these in a similar vein as to how Code Golf exists on Stack Overflow - it's a bit of a game compared to a normal question. Past the original author, it is unlikely to help many users outside of the sport of naming the items; this unlikelihood is amplified by how scattered the memory of the question asker is in providing known info. As well, any truly vague ones will tend to fester and accomplish nothing by staying open other than attracting yet more junk questions of similarly lacking detail.
So taking the above into account, if you do plan to allow these on your Stack Exchange site, exercise moderation and be cautious not to let this sport overtake your standard Q&A. It feels good to help someone out with something they forgot. But remember that our ultimate goal as a part of the Stack Exchange Network is to help the larger number of people in the internet, not to be simply a personal support line for individuals. Time spent helping individuals reduces our resources to help everyone else. As JavadocMD put it wisely in a chat message,
[...]it's easy to forget that each question has a real cost: the cost of clutter and the decrease of visibility for all other questions