What does the "i" in Apple product names mean?

iPhone, iPod, iPad, iCal, iLife, etc. Does the "i" mean anything? And is it a trademark for Apple?

When Steve Jobs first introduced the iMac in 1998, he proclaimed that the i stood for Internet. Jobs went on to say, "i also means some other things to us" and displayed a presentation slide with the keywords:

internet
individual
instruct
inform
inspire

You can even view video of this event.

The "i" was first used on the iBook and iMac. These were produced as Steve Jobs wanted a pro and consumer model of a desktop and portable computer. This later rolled out with more products, iSight, iPod, iPhone, iPad.

Yes the products are trademarked, but using an "i" itself before a product is not trademarked and it cannot be. Here is Apple's trademark list

According to Wikipedia (for the iMac at least):

Apple declared the 'i' in iMac to stand for "Internet"; it also represents the product's focus as a personal device ('i' for "individual").