Dominus points out that this game is commonly known as "Geography." Though he's right, I have to say I still prefer "Gallivanting."
He goes on to provide evidence that word games can be of use to mathematicians and computer scientists:
I can't find my references, but computer scientists have demonstrated that the `generalized' version of this game is `intractable' in a well-defined sense. That is, either there is no efficient way to compute a winning strategy, or else there is an efficient way which would automatically translate into an efficient solution for a lot of other intractable problems that experts have never been able to solve efficiently.
To understand the `generalized' version first you transform the parlor game into a paper-and-pencil game, as follows: There are 26 circles, labeled `A' through `Z'. For every country (or other permissible geographic feature) there is an arrow leading from the appropriate starting letter to the appropriate ending letter. So, for example, there is an arrow from `E' to `D' labeled `England'. The first player picks any arrow, inks over it, and places a penny on the circle it leads to. Thereafter, the player whose turn it is moves the penny along any outgoing arrow that isn't already inked over into the circle at the other end of the arrow, and inks over the arrow they just used. If the penny is in a circle with no uninked arrows at the end of your turn, you lose.
Now, replace the 26 circles and their arrows with an arbitrary collection of circles and arrows; that's the `generalized' version.
Nancy Mandel points out that "according to Mapquest, there are three places called Keokuk in the US, and one Keokuk Falls." That name does sound vaguely familiar, and apparently it's a popular one... Still, I suspect the one I listed on the answers page is more familiar to more people. But I do like this alternate answer.
Dan Tilque notes that Hawkeye and BJ play Geography in an episode of Mash; they go from Los Angeles to St. Croix to a Mexican town that starts with X.
He suggests another good strategy for dealing someone giving you York or New York and thus landing you on K: respond with Kiev. He notes that J and Q are particularly difficult to get to; Cluj, Romania, is one of the few ways to get to J. (Although I'm sure it's not true, I'm inclined to suggest that that city is the birthplace of the Kludge...) He adds, "There aren't any largish places that end with Q. Qaanaaq, the palindromic Inuit name for Thule, Greenland won't do because you have to be on Q already to use it."
(Last updated: 10 February 1998)