Repairing Speaker Foam Surrounds?

bigmush asks: "I have an old pair of speakers, and they had been working fine until recently. I took off the covers, and saw that the foam surround had started to wear out on both of the woofers. After 15 years of service, this was a sad discovery (though also an opportunity to justify an upgrade!). I found a few foam surround repair kits available online. How well do these work? What experiences have you had with them?"