I have extolled the virtues of Firefox and Thunderbird in another section. Suffice it to say that these two versions are not direct releases from Mozilla but instead have been modified by PortableApps.com (see above) specifically for use on portable USB devices.
I must have been adrift at sea or out in the ozone lately because I only recently discovered that there is a portable USB version of the Opera web browser. It is not available on Opera's own site; instead, the portable version is offered by an Austrian programmer named Markus Obermair, whose web site Opera@USB claims that he has "the authorization of Opera … to offer a changed Opera version for flash/USB device[s]" and that his product has been tested by Opera. Authorized or not, all I can say is that it seems to work just fine, and I am tickled pink that the second-best web browser in the world (after Firefox) is available in a portable USB version. Yippee-kay-ay! [Added 27 April 2010]
Based on Microsoft's Internet Explorer engine.
Based on Mozilla Firefox engine and therefore can directly use the "bookmarks.html" bookmarks file exported from Firefox. K-Meleon is certainly not as full-featured as Firefox with add-ons, but if you do not want to wrestle with the complexities of setting up Firefox Portable while still retaining all of your Firefox bookmarks, this is an excellent alternative.
Note: when you run the installer, be sure to UNcheck the option "Multi-user Profiles" so that your profile data will be stored along with the program files on the USB device rather than in the host machine's "Documents and Settings" user folder.
A free, open source web browser that can also import all your favorite bookmarks from Firefox's "bookmarks.html" file.