Cyril Morong and Dave Petit document the teams that have taken the biggest drops in winning percentage from the first half of the season and in the second half at Beyond the Box Score.
Thr 1879 Cubs played the first half of the season at a .769 pace, but played the second half at .400.
If you want to go for "modern" times, you can look to the 1905 Cleveland Indians which started at .636, but played the second half at a .351 pace.
The 2006 White Sox project to be 22nd in this category. The 2005 Nationals started out at .617 and played the last 81 games at a .383 pace. And if you look at those numbers, you can tell that Washington had to finish the season at .500.