What if they had been Queen?
Empress Matilda
As her son, Henry, acceded to the throne after Stephen, Matilda's being Queen wouldn't have changed the succession. However, if she, as a woman, had become a reigning monarch in the Twelfth Century, then it is possible that we may have seen another queen before Mary I in 1553. Also, if Matilda had been a successful queen then perhaps future kings, such as Henry VIII, would have been less concerned with the need to provide a male heir to the throne.
Lady Catherine and Lady Mary Grey
Although there was a good chance that either Catherine or Mary would become Queen, neither of them aspired to the throne and after the failed attempt to make their sister, Jane, Queen they could not count on a great deal of support from nobles who had no desire to lose their heads. Furthermore, neither of them was deeply Protestant, like Jane, and therefore they weren't a viable alternative to the Catholic Mary I. As it turned out, neither of them lived long lives and it is likely that even if they had ruled, the reign would have been brief and relatively insignificant.
Arbella Stuart
It is difficult to say whether or not Arbella desired to be Queen. On one hand she never made any attempt to seize the throne but she had been raised as royalty and her romantic assignations suggest ambition. Even if she had been named as Elizabeth's heir, James would almost certainly have tried to claim the throne himself and, as a man and King already, would have garnered considerable support. If James had died young, his son, Charles would have eventually tried to take the throne. As her claim wasn't as strong as theirs, it would have made for a very unsettled reign for Arbella.
Princess Charlotte
Charlotte's death left the king without any legitimate grandchildren and his other sons were urged to marry. George III's fourth son, Prince Edward, dismissed his mistress and proposed to Leopold's sister, Victoria. Their daughter, Princess Victoria of Kent, born in 1819, became heir and then Queen. Her uncle Leopold helped arrange her marriage to his nephew, Albert of Saxe-Coburg and Gotha. If Charlotte had not died then Victoria may never even have been born, and our current royal family would be descended from Charlotte instead.
