Very interesting questions, all.
First of all, let me say that I personally like the looks of damascus (pattern-welded) steel, and really love many of the fine examples that have been posted.
Then, onwards, with the rest: a while ago I took to surfing the internet to understand better what damascus is, and if the additional premium that you usually pay for it was really worth it from a purely performance point of view.
My understanding of all the material I read boils down to:
- ancient damascus was wootz, western bladesmiths were so impressed with it that they tried to copy it, got mislead by its appearance and arrived at pattern-welding as a way to replicate its appearance, but not its performance
- wootz and pattern-welded damascus are made by totally different processes
- pattern-welding is mainly for artistic/beauty purposes, but in the hands of a good bladesmith can yield a knife as good as a single-steel one
The only hard reference I recall claiming that pattern-welding damascus may actually be superior to a plain carbon steel blade is by Bill Bagwell in his book on battle blades etc. (I am assuming that Mr. Bagwell refers to pattern-welding damascus - I do not think he actually goes out and say that, though)
That said, I only have some pattern-welded damascus blades by Kevin Cashen, Tom Ferry, John Christensen, John Fitch, and have never had the courage to actually do any performance test on them against similar plain carbon blades; nor do I have any wootz blades, or any experience on mosaic damascus.
The point which was made by Steven Garsson and Anthony Lombardo on pattern-welded steel being more rust-resistant is one I've heard several times and that seems entirely reasonable; it also chimes perfectly with something which Jim Rodebaugh once said to me about making an extended (I think it was a couple of weeks in Alaska, but I may be wrong) hunting trip with a carbon steel and a pattern-welded damascus bowie, both functional pieces which were there to be used, and used hard; they performed pretty much the same, but at the end of the trip the damascus one simply had to be wiped and little less to pretty much restore it to its previous state, while the carbon steel one had be subjected to a much more serious maintenance treatment.
The other point which was raised by some about (good) pattern-welded steel being comparable or even superior to differentially tempered plain carbon steel is another one which looks very reasonable on the surface, but does not really chime with my understanding, which is that (good) pattern-welded damascus can get to be as good as plain (good) carbon steel, not really superior from a purely performance point of view. On this, though, I may be wrong, and would be very interested in getting to see what is the consensus on this, if there is one. I would love it if there were some sort of magical steel which is the end-all be-all, but if there is one thing this place has taught me over the years, is that there is no such thing

! Just different trade-offs....
Here's some links which may be of some interest (some are pretty arid going

):
http://en.wikipedia.org/wiki/Damascus_steel (obvious starting point)
http://damascus.free.fr/index.htm (site with a lot of info on the different types of damascus - difficult to navigate, though, in that you have to browse most all pages to get to what you want)
http://www.tms.org/pubs/journals/JOM/9809/Verhoeven-9809.html (seminal scientific article by Verhoeven & Pendray)
http://users.ntsource.com/~bluedevil/ Tribune_damascus_steel.htm (journal article popularising some of Verhoeven/Pendray results)
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/advanced/t5_1_1.html (just stumbled on this, but it looked like a nice summary)
Best,
Guido