Statelessness is a kind of negative state (falling through the cracks as it were) so I am not sure a full list can be created but here are some (actual, not merely theoretical) cases:
- Born to parents who are themselves stateless.
- Born to an unmarried mother with a citizenship transmitted solely through males (a common problem, there are dozens of those).
- Born to parents who cannot transmit their citizenship for another reason (e.g. British citizens by descent, under certain conditions, although that can usually be fixed, indeed that's what the form S2 referred on the page you found is about).
Of course, this would only apply if the birth in question happens in a country with strictly no jus soli and no fall-back clause. I don't know precisely how common this is elsewhere but in many European countries, even those that are comparatively restrictive about dual citizenship and jus soli, the law stipulates that someone born to unknown parents or with no other citizenship is a citizen (there are exception, though, like Austria).
The Americas generally have unconditional jus soli so the problem does not arise there at all.