The nineteenth century was an age of spectacular sacrifices and flamboyant gambits that resulted in the kind of wild games that we rarely see in modern practice. Following are two king chases from the glory days, one from modern tournament play, and one from chess.com.
Good manners, the lubricant that allows people to rub shoulders without too much friction, appear to have become a thing of the past. For most of us, anyway. Of course, in the case of another outdated institution—the monarchy—you would expect good manners, if little else. So when a king exposes himself in public he's not going to get much sympathy from me if he gets punished for it.
In this 1844 game between a pair of Alexanders (a kingly name if ever there was one) Alexander Hoffman's king flaunted himself in front of Alexander Petrov's army and was sent to Coventry for his indiscretion.
Twenty years later William Steinitz took the white pieces against the ubiquitous Mr No Name. The Evans Gambit gives Black plenty of chances to go wrong and our anonymous gladiator was adept at finding them. He would have been able to boast to his grandchildren that he won Steinitz's queen but that was the last time in the game he had any choice at all.
If you thought king hunts like those don't happen in the modern era you need look no further than 10 year-old Joshua Waitzkin (of Searching for Bobby Fischer fame). His opponent, IM Edward Frumkin, played 24...Nb2 attacking Waitzkin's rook on d1. Rather than move the rook, Waitzkin removed its protection with 25.Re3 allowing his opponent to win a whole rook. Perhaps Frumkin didn't see what Waitzkin planned, or perhaps he just didn't take such a small boy seriously enough, because he captured the now unprotected rook—and World War III broke out on the king-side. This was blitzkrieg with no quarter given and after Waitzkin followed up with a queen sacrifice on move 26 he had a perambulating king and a forced mate in six. Spectacular stuff!
To round this off I'd like to point out that you don't have to be a GM to chase kings. I've done it myself. In fact, I did it right here on chess.com. In the following position I chased RobinsonGeorge's king all the way from f3 to g6—then resigned! Why? Because I'd helped him get to a square where there were no more checks possible and where his king supported mate in two different ways: Rc8+ or Qxe6+. We played that game in November 2007 and I still haven't forgotten it. I'm glad to say George is still with chess.com and still playing actively.