I wear Asics for everything--Fortitude running shoes and Blackheath cleats.  Asics is the only shoe I've found so far that has helped eliminate Achilles and knee pain.

I use the 160Tr for weight lifting and twice a week when I work with a trainer doing leg exercises that include speed and agility training.  I'm on my second pair (third if you include the 150 Trs I had first).  These shoes hold up really well.  They are leather (synthetic?) so they're a bit heavier than a running shoe but not nearly as heavy as many other cross trainers.  I find them very comfortable.

I've had trouble with most other brands causing foot pain, but never with an Asics.