I've always questioned to what extent this stereotype was true.
http://news.discovery.com/human/psychology/voter-conservative-aging-liberal-120119.htm
I think in
some ways people do get more "Conservative", but not in the way most people would assume.
"Today's liberal is tomorrow's conservative" is true in the sense that the word "Conservative" refers to being in favor of the status quo. However, what's considered the status quo today isn't necessarily the same status quo as in the past or the future. Today's Republican/Conservative is very different from the Republicans of 50 years ago (for better or worse), and the Republicans we'll see 50 years from now will be very different from the Republicans we see today (for better or worse).
In other words, the definition of "Conservative" varies relative to each generation. Each generation has their own values and problems to deal with depending on the environment they grew up in. Russia's "Conservatives", for example, are more left wing and seek to reestablish the values of the Soviet Union.
So while it's true that today's youth may consider themselves "Conservative" in the future, chances are the word will be more associated with the status quo they grew up in at the current moment (again, for better or worse).