There are several situations that can happen if Henry VIII is never born :
1°) If Arthur Tudor survives, then he would rule. However, this does not necesserarily need Henry VIII to never been born since Arthur was older than Henry VIII.
2°) If Arthur Tudor dies as happened OTL (meaning before Henry VII), the crown passes to Margaret Tudor, wife of James IV of Scotland. We thus have an earlier United Kingdom.
3°) If Henry VIII is not born because his mother died in childbirth while giving birth to Arthur (as proposed by Gustavus Adolphus) and Arthur dies like OTL, then we have a major succession crisis after Henry VII's death, unless the King remarried and had other children. If not, Arthur would have been Henry VII's only child and thus Henry VII's successor would be far from clear : this might restart the War of the Roses, although I'm not sure if the Lancastrians have any valuable candidate left for the throne...
Anyway, Henry VIII not ruling would have interesting butterflies.