(Written in March 2009 for an XKCD forum thread on the subject.)
I'm a writer of short stories. I don't write novels, although I think I could if I wanted to; the form doesn't interest me much at this point. To me, one work of fiction should express one idea as powerfully as possible, and the extent to which length can help that is actually rather limited.
What I wouldn't say is that you can't learn a lot about writing that applies equally well to novel-writing by writing short stories. To write a short story, you scrutinize every detail of the prose, of the sequence of the story - how to express ideas as efficiently as possible, how to recognize where "show, don't tell" is meaningful and where it's crap... and if you write short stories, you get feedback much faster than if you write novels.
So, I'd say - anyone who wants to write prose should take some time to write short stories, in the sense that they should force themselves to stretch their abilities; that they should write experimentally, with strange and limiting premises; that they should study how to maximize dramatic effect with a minimum of words or even with a minimum of information. It'll give them, the novelist, a deeper understanding of their medium.
What it won't give them is, of course, that necessity - practice.