How to visualize a phylogeny with thousands of tips?

What abilities should a phylogenetic visualisation tool have? What is important when you have so many tips (OTUs) that it is too big to print out or even scroll through on the screen? I have several pieces of research in this last category. In no particular order here are some things that seem important to…

20,000 leaves on my tree

Apologies to Jules Verne, but on 30.10.07 there were 20,363 Metazoan SSU rDNA accession numbers in the Silva 92 database. My immediate questions- can a reliable phylogeny be constructed from this by a biologist with average computing resources? Can the resulting tree be informative (or is it too big to get any meaningful information onto…