I appears people have worked around the UNO problem mentioned on this page. I do not appear to be able to edit it, even though it is a wiki.
As of now, you can. Actually, apparently the big problem with the UNO is the auto reset - if you put about a 120 Ohm resistor from reset to 5v on the UNO then it'll work.
Load the ISP sketch, disable the auto reset with the resistor, and then follow the normal directions.
(I just burned 3 chips last week from my UNO - so I know this works).
June 2011 Haven't tried it, but perhaps the fastest way to get ArduinoISP working on the UNO is to disable the bootloader. Then when the board resets it goes right into ArduinoISP. Note: you will want some way to re-enable the bootloader.
I would also love to see this page updated. I've been going around in circles trying to pull this off, finding lots of different (undated) tutorials with slightly different advice, slightly different hardware libraries, etc, none of which seems to work.
It tutorials had publish dates, or existed on a wiki, this would be less of an issue. The people in the small crew that actually can update this page, I'm sure are terribly busy.
The thing is that there are lots of "official" tutorials on the site with errors in them. Many members have been trying for years to get them changed but with little success.