What did 37 million people do on Tuesday?
Those ratings numbers are just outstanding. There are so many TV programs these days, and so many other entertainment options, that American Idol's continued (and growing) ratings success is just incredible. Personally, I watched season 3 fairly regularly and was totally addicted, so I've tried not to get too into the subsequent seasons, though I admit to following the show even when not watching regularly.
I'd guess that the "family-friendly" nature of the show is what leads to its large numbers, but that wouldn't really explain the 9:30-10:00 success. I'm guessing (hoping) that parents aren't keeping their kids up until 10 just to watch the first round rejects trying out in Minnesota.
What's more, the fact that there are so many entertainment options available should actually diminish the importance of being family-friendly. The classic example is that of apple pie, which for years was America's favorite desert. (Note: this analogy is someone else's, but I can't remember where I heard/read it, despite the vast resources of the internet.) One story for the decline in popularity of apple pie is that with advancements in refridgeration techniques, apple pie declined in popularity because while it was everyone's second or third favorite desert, it was not the #1 desert for many people.
Thus, when refridgeration techniques were less advanced, and it was only possible to store one desert for the whole family, apple pie was king. It was a great compromise. But once it became possible to keep 3 or 4 different types of deserts ready to eat, apple pie dropped off because everyone was able to choose their #1 desert. TV is not really any different.
In the days when families had one TV and no computers and video games, families watched whatever was best for the group as a whole, but now that there are so many different options available to everyone, the advantage of being "family-friendly" is gone. If you are the #2 option for everyone in the house, no one watches you. Before, if you were #2 for everyone in the house, there was a good chance that everyone watched you, as long as there was sufficient disagreement about what was #1.
So we can't explain American Idol's success as it being enjoyable for everyone in the house, but not everyone's favorite. With so many options and outlets available today, there's little need for compromise. If 37 million people watched American Idol on Tuesday night (and probably about the same number last night), then that tells me that over 10% of Americans think that's the #1 thing to do between 8pm and 10pm.