According to stereotype, yes. But not according to the data.
I’ve finally returned to my old suicide project, which had been moldering in a (virtual) drawer for quite a long time. With the help of a new co-author, I’ve been analyzing the results of a bunch of regressions. I was surprised to note that the variable for teenagers (percent of population from 10 to 19) consistently yielded negative coefficients, meaning higher teen population is associated with lower suicide rates. So I went back to the original data source (imagine that!) and found that the stereotype is dead wrong: suicide rates are notably lower for teenagers than adults.
Suicide rates do rise throughout the teen years, but they plateau at about age 20 and remain flat throughout the years 20 to 65. Then they jump again for the 65+ demographic.
So what explains the misperception? I glanced over the web resources on teen suicide, and by the numbers they technically do not seem to err. They note that suicides rates rise during the teen years, which is true, but it doesn’t indicate a particular problem among teens, because (as the graph shows) suicide rates remain high for adults. They also note that suicide constitutes a large percent of deaths among teens, but this is not terribly surprising, since teens are less likely to die of things like heart disease and cancer.
ADDENDUM: In case you're wondering, teen suicide rates have not been rising, either. They've been in decline since the late 1980s. (For this graph, I had to go beyond the years 1981-1998, which WISQARS maintains separately.)
[UPDATE: Graphic mysteriously deleted by Blogger now restored.]