My favorite factlet (I won't let things go!) is one of the most famous. The winner of the SuperBowl (NFC or AFC) predicts the stock market. If the NFC team wins, the market does much better than AFC team. I haven't seen the number in a few years, but the difference was not only "statistically significant" it was large, like 20% return difference.
It's a great example that if you look at enough random events with a 10% or 5% chance of being wrong, you'll find a lot of wrong statements.
What was also missed in the above is that the data set is small. NFC teams (Packers in 67 and 68) won in the 60's when the market was strong. Then AFC teams (Dolphins, Steelers, Raiders) came on in the 70's and the market did horrible in the 70's. When things got great in the go-go 80's and continued to the tech-bubble in the 90's, the 49ers and other NFC teams (Redskins, Giants, Bears and some nameless team in Texas) were dominating.
According to a wikipedia page, it has been right 33 out of 41 times. 80% accurate predictor.
The other interesting thing about this factlet is that you've got room to fudge data. Teams started in one conference and then switched.
The Super Bowl Indicator is a good example of "spurious"