To me, the most addictive app is Google Talk. You start by entering a few words (a common phrase, or a lyric) and google finds the next appropriate word, based on what's frequently found on the web. Then, the program drops the first word of your sequence, and searches again to tack on a new word at the end. The process repeats every few seconds.
It's good for surveying popular opinion (for instance, start with "George Bush is" and the program generates "the" ... and then ... "antichrist" ... before devolving into gibberish).
I've had more wholesome fun by typing song lyrics. I entered "everybody loves somebody" to get the next line of a Dean Martin tune (hey, I'm in a Rat Pack phase). Sure enough, Google Talk generated the appropriate next line, but in short order the lyrics morphed into a conglomeration of recent alt-rock hits, before settling into a loop of Pink's "just like a pill" (there seem to be sinkholes, or phrases that recursively clone themselves -- not unlike today's pop music!).
The term "blogborygmi" yielded "tracked: by the world news. And more"
GoogleTalk is like listening to the world free-associate.
So many other programs are also interesting. In Word Color you type in a term, and google sifts through the top image matches to find the most frequently-returned color. Not surprisingly, "sea" is blue, "money" is green, and "blood" is red. "Human," apparently, is brown, as is love and food. "Clear," if you were wondering, is kind of green.
When you're done playing, the site's author, Douwe Osinga, has an informed look at the the history (and future) of searching.