I know we have some very useful ones on cstheory.SE and I have seen some amusing ones on Stackoverflow. On other sites such as scifi.SE they seem to be banned.
What is our stand?
I think there are some natural questions that can only be answered appropriately by giving a list. Examples include
The proper way to have such questions on StackExchange is, imho, like this: There are few (at best only one) answers that are collaboratively maintained. If users mistakenly add superfluous answers, they are asked to incorporate their answer as item into the main answer. If they don't cooperate, their answer is deleted for them.
The danger is that people add low-quality content to the main answer where it can not be downvoted. Maybe the process can be adapted (add as new answer; upvoted answers are incorporated, others only deleted) to keep that in check?
List questions generally do not work well on Stack Exchange. They are generally banned on Stack Exchange:
I happen to have direct experience with list questions, having active on Scifi.SE since day one and a moderator there for most of that time. This is our best list question, kept around for posterity. Note how most answers list just one item; the voting on the answers does not convey any useful information; the list is woefully incomplete. After seeing many such questions (only usually with even more incomplete answers), we decided to specifically ban them.
List questions on Stack Overflow have long been frowned upon, and are officially banned. Old ones have often attracted a large collection of low-quality answers. New ones are generally closed (unless they fall through the radar, always a possibility with ~5000 questions daily). Older questions are sometimes kept around because part of the SO community is dead set against deletions, but this should not be taken as evidence that these questions would be accepted if they were posted today.
The Literature site has a limited book recommendation policy. In a nutshell, book recommendations are allowed if they are reasonably specific and encourage answers that describe a curriculum rather than a single book. This policy has had mixed results; the quality of these questions is usually not very good but the bad ones can and do get closed and a few get good answers. Programmers has a different book recommendation policy which is somewhat similar in spirit; on Programmers, a vast majority of incoming questions do not meet the policy.
Researcher communities are somewhat unusual; what works on CSTheory is unlikely to work on a less elitist site.
I do not see a reason to deviate from the usual Stack Exchange policies. No list questions.
(Questions about lists are welcome, of course. Data structures are on-topic here.)
I'm starting to get really tired of seeing these "list question" discussions come up... "List question" covers a lot of not-very-related question types, and usually ends up confusing someone who sees the discussion and thinks, "But what if the answer to my question just happens to be... a list?"
There is some very specific guidance in the FAQ on every site:
The first three of those tend to result in lists. But... that's more of a symptom of an underlying problem, aptly noted by Gilles in his answer: these are "questions" that don't really have answers.
Stop fixating on lists. Avoid questions that aren't really questions.