Opera 10 Final is also natively portable. I couldn't extract it, so I installed it under Sandboxie, then copied everything to a folder. I thought it wasn't portable anymore, but then I tried changing the "Multi User" value in operaprefs_default.ini.
I'll give a detailed explanation so that any John Q. Computeruser that comes by should be able to do this (and perhaps for the description in the database, if it gets added).
1. Install to default directory.
2. Copy the contents of "C:\Program Files\Opera" to a folder on your portable drive
3. Copy the contents of the %APPDATA% folders to the same folder you put the program files in.
On Vista, it's "C:\Users\<YourUsername>\AppData\Roaming\Opera" and "C:\Users\<YourUsername>\AppData\local\Opera"
On XP, I think it's "C:\Documents and Settings\<YourUsername>\Application Data\Opera" (I can't believe I'm already forgetting).
4. Uninstall the installed copy
5. In the folder you just copied everything to, change the last line in operaprefs_default.ini from
Multi User= 1 ;
Multi User=0 ;
6. Run opera.exe
It saves settings to the application folder, but it still writes that one registry key:
"Last CommandLine v2"="F:\\UninstalledApps\\Opera\\opera.exe "
If you're worried about slowdowns or excessive writes to flash memory, you can disable disk caching by going to Tools -> Preferences... -> Advanced -> History