I planted some Asparagus "roots" (i.e. not from seed) last spring in
my garden. I read from various sources in the 2nd year and even 3rd
to just let them grow and not harvest them. I am finding them tall
(24 to 30 inches) and spindly. They are even falling over. Is this
proper? It does not appear that they have propagated much (only 2 - 8
separate shoots in each mound). I would have though they look
healthier and flourish more in this 2nd year.

Any assistance appreciated.
Mark.

I am finding them tall (24 to 30 inches) and spindly. They are even
falling over.

You are aiming for about that height (probably a bit taller actually),
but with a solid wall of leaves. For example:
http://www.knpr.org/dbloom/images/asparagusbed.jpg
http://z.about.com/d/gardening/1/0/a/G/Asparagus.jpg

Where I can't help you so much is how many years it takes to get to
that point, and whether your slow progress means you should be
fertilizing or looking for a pest or whatever the problem might be.
My (limited) experience with asparagus was with a well-established
bed.