Audacious Epigone has calculated a good answer to an old question: When was The Simpsons at its best? He averages by season the rankings of individual episodes on IMDB.com, which is a pretty reasonable approach. IMDB ratings are biased toward the tastes of youngish male fanboys ("Worst. Episode. Ever."), but who better to evaluate The Simpsons? And they aren't rating seasons as a whole, just individual episodes, so any preconceptions the raters may have about which was the best season enter into the process less. Sample sizes for individual episode ratings are typically in the 500 to 900 range, which aggregates to over 10,000 per season.

The curve for the first eleven seasons is pretty elegant. The average episode's rating goes up each year from season one to six (with seasons five and seven almost as great), then declines every year through season eleven. The peak years were 5-7 and the big dropoff was in 9-11.

That would fit with my subjective impressions: the show just kept getting better for a number of years, then reached a remarkable peak of consistent excellence in the mid to later 1990s. 

The curve of the first half of the graph is very similar to a professional athlete's career, even though The Simpsons were largely a collective enterprise with a fair amount of turnover among writers.

Off the top of my head, the athlete with the most similar-looking career productivity graph might be Chicago Cub Ernie Banks, who started out as a slugging shortstop, a rare and valuable combination, then blew out his knee and had to switch to first base, where his offensive productivity no longer made him exceptional. But his personality made him popular in Chicago,  and playing in Wrigley Field inflated his statistics, so he had a long career even after his prime.