We all know that one of the craziest personal unions in history wound up because of well, who the Hell knows what everyone involved was thinking.
Henry VIII's third wife, Jane Seymour, died in 1537 giving birth to his son and heir, Edward VI. Henry sent his ambassadors abroad that December already to sound out princesses. There were limited options available, since Henry wasn't exactly everybody's favourite idea of a son-in-law, what having "poisoned" his first wife, then married a schismatic and had her beheaded and then the doctor's incompetence in wife no. 3's childbirth.
He probably wouldn't have been able to find a new wife abroad had it not been for the king of France and the emperor being at their usual boxing match. The king of France's candidates (his daughter Marguerite or the Dowager Duchesse de Longueville) seemed to be in the lead. That is, until the emperor found out about his own candidate, the dowager duchess of Milan (who had refused Henry) plotting to marry her sweetheart, the Prince of Orange (or at least, so the story goes). He offered the dowager duchess to Henry, again, this time with the duchy of Milan to sweeten the pot for the dowry. The duchy was to devolve on Henry and Kristina's son.
How or why Henry thought that far-off Catholic Milan was a good idea is still debated. The Tudors had no claim to the duchy, and certainly no Milanese ancestry. But land is land, and Henry probably agreed to it, with the intention of trading it for something a little closer to home at some future date.
Either way, as we know, that never happened, and Kristina became Queen Christine of England. And lo and behold, by the time of Henry's death in 1541, she'd popped out three children, a boy and twin daughters. The boy, Henry, was immediately named 'duke of York' although Karl V took his sweet time handing over the duchy of Milan (it led to some long-running conflict between England and the Empire for a while) to it's duke, Enrico I.
Of course, things got even crazier when Karl V's niece/daughter-in-law, Maria Manuela of Portugal died in childbed with a daughter in 1545, his son, Prince Felipe remarried to Henry VIII's daughter by that schismatic, Anne Boleyn in 1548,and Enrico got his duchy in Italy.
Everything seemed fine. Until King Edward VI died without children. And suddenly the Catholic but technically Anglican "half-Danish popish runt" (as some historians have referred to Henry IX on account of his small stature) was heir to a Protestant throne. Enrico was next in line, but he was a) a Catholic (or at least viewed as such) and b) he and his mom (serving as regent in Milan) hadn't set foot in England since he was 4yo (he was now nearly forty); and c) was only heading there now, because the French were occupying his duchy and he hoped to use English soldiers to get it back.
So, what if Henry VIII hadn't been thinking with his little head (because, let's face it, Kristina was a beauty, I'm not sure he gave a damn about her intelligence)? Or Karl V never forces his niece to marry the king of England? Who would Henry marry? Who would get Milan? Would Felipe II and Elizabeth Tudor still marry? Would his sister Mary still end up under house-arrest for much of Edward's reign? And would Edward still die without children?