Good advice that I got from the book "Personal Finance for Dummies": Insure for disasters. Anything else, self-insure.
Insurers price to cover their expenses and make a good profit. If you can comfortably cover the loss, in the long run, over many products, you should be able to accrue the insurer's expense charge and profit for yourself. And you will also save the bother of dealing with the insurer (time and annoyance).
Of course, there are some exceptions, depending on device and/or person and usage. E.g., Mark's experiences. Or cellphones owned by people who use them very heavily, or who are clumsy with them. Certain devices that are, or appear to be, more prone to failure (e.g., jetBook?, certain DVD recorders, maybe large-screen glass eInk readers], etc.).
And if you're handy, the web now has disassembly and repair instructions for most electronic devices.
I got talked into buying a $30 extended warranty for a $100 Sony PDA in 2003. The salesperson said it's a no-brainer because the battery fails within two years, so it more than pays for itself. Still waiting for that battery to fail, or the PDA to fail.