I never understood the name "iGoogle". You know what the "i" in Apple's products and many other company's products mean? Internet. So Google called the product "Internet Google".
According to iMac's history on Wikipedia[2], "i" stood for "Internet". (Again, same logic can be applied to the iPhone and iPad. No idea about iPod, which came after iMac but before iPhone and iPad)
[1] This is my personal opinion. [2] http://en.wikipedia.org/wiki/IMac#History