For years web browsers came with nice throbbers. Not anymore. Now you mostly get a little black wheel thing in the tab. In Opera I like the pop-up progress bar when things are loading, but that's not a throbber really, but that's OK because we all love Opera for being different.
I always liked the old Netscape ship's wheel splash screen and the comet throbber. On dialup you got to watch those comets fly for a very long time. At least they were pretty. You could even change the throbber to something cute, like a running dog with a newspaper in its mouth.
Way back in the dark ages, I used to watch the planet-and-nodes throbber on the NCSA Mosaic browser:
By far the best throbber ever was the Mosaic "folding panes" throbber. It goes way back but was the one I saw first and always liked the best.
In the screenshot below, you can just barely see the folding panes in the upper right corner, but they aren't moving because it's just a screenshot. They were pretty and I remember being in awe the first time I saw somebody fetching graphical webpages with this browser. If anybody ever sees an image of the moving "folding panes" throbber, please let me know.