Synopsis: Opera is a fast and secure web browser that features pop-up blocking, tabbed browsing, integrated searches, built-in email and RSS client etc. OperaUSB is a portable package for Opera that does not write to the registry nor leave any data on the guest machine where it is run.
Another alternative is Opera Portable. Thanks to TheReaper for suggesting this.
Writes settings to: Application folder
How to extract: Download the ZIP package and extract to a folder of your choice. Launch operausb.exe.
Stealth [?]: Yes
Unicode support: Yes
System Requirements: Win98 / WinME / WinNT / Win2K / WinXP / Vista
Screenshot - Download