The 10-digit, geographically-based phone number
Imagine if someone who was interested in futuristic technology went into a coma in 1966, only to wake up 45 years later in the modern day. "Rejoice!" you might say. "Remember the handheld communicators in the science-fiction movies of your era? Well, we have them now, and they're even smaller than you imagined! Almost everyone in the developed world carries them in their pocket, and you can talk to anyone, from anywhere, without wires!"
"That's amazing!" he'd reply. "Say, how'd they solve the problem of identifying the communicators? How do you tell your handheld device which other device you want to contact?"
"Oh," you reply, "you just give it your phone number."
"Wait, phone number? Like ... phone number phone number? Like, the same as on my phone? My phone hanging on the wall of my kitchen?"
The fact is that your futuristic handheld Star Trek-style communications device is still using an identification system that your grandmother used to make calls on her party line. In fact, thanks to the magic of phone number portability, your cell phone might be using the actual number your grandmother used back in the day.
And herein is a valuable lesson as to why zombie technologies persist in ways that technophiles find baffling. New technology often flops if it wipes the slate clean and only references itself, without integrating into people's existing lives. Imagine if the first mobile phone users were only able to talk to each other! Those first bulky DynaTACs were useful because they integrated with the existing communications network -- in this case, the system that had built up in stages over the previous century to route calls from wired telephones. In 2011, more and more people are untethering and going wireless-only; but even if someday the world goes wireless, all our technology will be so invested in this decades-old system that it will be difficult and pointless to change.
One other major advantage of the 10-digit phone system (and its equivalents outside of North America) is that it's a government-mandated standard. Several wireless communications providers do try to bypass it when it comes to text messages -- BlackBerry's BBM messaging service and Apple's new iMessage communicate via the Internet rather than the phone network, and you can use iMessage without a phone number at all. But these are closed, proprietary networks, and will never be able to replace telephone numbers for universal communications purposes.
Oh, and one last quirk of using a 10-digit number with your mobile phone: in North America, anyway, the number encodes information about where you live -- or at least when you got the phone. Young people are among the most mobile and among the most likely to use they're cell phone as their primary phone; many refuse to go through the hassle of changing their number when they move and are left with phone numbers from one or two cities ago. (Many other countries have nationwide area code equivalents dedicated solely to wireless numbers.)