I'm a Volvo 240DL owner.  My car is a '86. A box.  I would like to
replace it with an updated version of basically the same thing.  By
that I mean something more or less square, very safe, little frills,
stiff ride ---that will last forever.  I don't like the current volvo S70
and S80.  They are too rounded, ie. they look like everything else and
aren't particularly known for safety and longevity.  Is there a
knowledgeable car geek out there who can pull together some safety, longevity
and "squareness" facts.  Ultimately I want to buy something used for under $20,000.

If you like square, get a Scion. A very cool looking little ride in my book.

http://www.edmunds.com/media/roadtests/firstdrive/2004/scion.xaxb/04.scion.xb.f34.500.jpg

tutuzdad-ga

Assuming your brick is dead or dying, what's wrong with another 240?
Or a 740 or 760? I got a late 80s 760 turbo intercooler that I love.
It's a bit more trouble than the 240 I replaced-- more complicated
means more to maintain, and the turbo is a pain-- but it's a sweet
ride that flies.

This might help regarding safety : 
http://moneycentral.msn.com/content/Insurance/P63955.asp

I must say, that Volkswagen are also known (or have been known), to last. 

However, the design is pretty "average" (like everybody else).