As I signed up for twitter during a period of "high maintenance" (that's polite for almost-constant brokenness), I encountered the fail whale quite often---and learned to like it, in its own way, because it had become a tradition of sorts, like fathers chasing kids around with power tools.
Twitter's Charming "mascot", the Fail Whale
And funnily, every time I visit the page in my Firefox instance, the Awesomebar keeps reminding me of the times when the whale was ubiquitous:
How nice: Nostalgia 2.0.