It was an early introduction for me to questions of statistical evidence. I'm a statistical omnivore. A lot of pundits aren't — they suggest it's in bad taste to notice patterns until a blue ribbon commission has certified them (and then they usually try hard to ignore the findings of the blue ribbon commission).
For me, though, you can find evidence everywhere. If 7-1 Wilt Chamberlain could average 50 points per game in 1962 by being more gigantic than everybody else, but by 1972 he couldn't, that suggests something.
In the 1970s, it was assumed that the future of basketball was ever-taller players: Kareem Abdul-Jabbar (7-2) was taller than Wilt, and Magic Johnson was a 6-9" point guard as a rookie in 1979.
Or, 6'4" and 235 pound Los Angeles Rams quarterback Roman Gabriel (who, interestingly, was Filipino on his father's side) was famous for his immense size during the early years of his NFL career (1962-1977). Late in his career, that didn't get mentioned as much.
In 1962, 5-10 Yankees pitcher Whitey Ford went 25-4. Today, only about 5% of major league innings are now pitched by pitchers between 5-10 or 5-11 (no big league pitcher in 2008 was shorter than 5-10). (Yes, Pedro Martinez is only 5-11, but then he's Pedro Martinez.)
But, it's not as obvious anymore that people are continuing to get taller from generation to generation in America.
NBA players don't appear to have gotten taller over the last 20+ seasons. In the 2008 season, the average height in the NBA was 6-6.98, down from 6.736 in 1986. (However, players have the right to be listed either with their heights measured either with their shoes on or off, which makes a difference of about 1" to 1.5" — I don't know whether there has had any effect.)
Similarly, high school seniors aren't clearly taller on average than their parents or teachers, as you used to notice.
So, I can't tell from incidental data whether people are now getting modestly taller or are staying the same size. Thus, we need blue ribbon data for this.
The government periodically collects "anthropometric" data on a large sample of people. By comparing the 1988-1994 study to the 2003-2006 study, we can see that over this 13.5 year (on average) stretch, young men of each race tended to be a little less than half an inch taller. In 1988-1994, non-Hispanic white men of age 20-39 averaged 5-9.95 versus 5-10.4 in 2003-2006, for an increase of 0.45 inches. That suggests a growth rate of about 1 inch per generation in recent years.
Among blacks 20-39, average height has grown from 5-9.75 to 5-10.1.
Among Mexican Americans, from 5'7.0 to 5-7.2. (Immigration tends to keep Mexican height down.)
So, I think the explanation for height stalling out in the NBA is that the influx of foreign players is balanced off by the decline in the number of U.S. born white players. The NBA's American players are drawn from a more limited population today (essentially, African-Americans) than in the past, so players have gotten a little shorter.
In 1972, the future of the NBA was assumed to be ever taller Kareems throwing in unblockable Sky Hooks. My guess is that better coaching has somewhat neutralized the huge advantage that giant centers had in the earlier days of the NBA, but I'm not convinced of this, mostly because nobody ever figured out how to neutralize Kareem himself. He was 3rd in the MVP voting as a rookie in 1970, went on to win six MVPs, and was fifth in the MVP voting as late as 1986. He was Finals MVP in 1985.
Kareem was kind of boring, but he was just insanely effective. So, I'm still baffled why there weren't more tall, thin, hook shot-shooting centers after him. When young, Kareem wasn't considered so much a once-in-a-lifetime freak of nature as The Next Stage in the process. But there hasn't really been a Next Stage since then.