The effect I was looking for doesn't seem to have a commonly accepted name, but does go by
dynamic grid layout and
cascading grid layout.
I haven't found a nice server-side component yet, but with ryanb31's help my searches for
jquery tiling did lead me to these, and a client-side component might do the trick.
Masonery[
^]
Isotope[
^]
There is also a commercial component called Packery.