I personally would say 'cell phone number.' In general, 'mobile' (BE) = 'cell phone' (AE).
'Cell number' sounds to me more like a shorthand label for a field in a small address book or database. In conversation I would call it colloquial or informal, since it's not really technically correct (it's not about counting amoebas under the microscope, or finding a prisoner in a jail). 'Cell' alone, without 'phone,' may already be spreading fast among young people, techies, etc. who live with the things glued to their ears, but I'm not convinced it's the most standard option for all audiences. (Yet. But check back in a couple of years; this area of language and culture is changing fast.)
'Cellular phone,' however, is too far in the other direction, maybe not unlike 'mobile telephone' in BE. The long form 'cellular' is already almost outdated nowadays, except perhaps in a very formal context with legal implications, like the generic description of a product, patent language, etc. (And maybe in bad translations from Spanish, where 'celular' is the normal word for the device.) I doubt it really needs to be listed with 'number' at all, though it wouldn't be exactly wrong.