I feel very stupid, but I just spent an hour reading through the manuals, searching, and so on, and I can't find a way to make stemless notes (as they are often used, for instance, to indicate pitch sequences in a text-based discussion, or as an aside in a score to indicate perhaps an uncommon scale, etc.).
There must be a quick and fast solution, given Lilypond's awesome power, but I just can't seem to find it. The closest I got was to override Stem.thickness, but apparently it cannot be set to 0---a faint stem is printed nonetheless.