A variant (invented independently, of course!) of [Dignan]'s "No more phone numbers...", this idea would see phone numbers composed of both letters AND digits. In other words, each position in the number could take any one of 35 possible values (9 numbers [zero is excluded - see below] + 26 letters).
As in the hexadecimal system, letters stand for two-digit numbers, so A=10, B=11, C=12, etc.

Dialing would be accomplished by pressing the "modifier" buttons on the bottom row of the keypad (*,0, or #) to indicate which letter on the button is to be used. For example, BIG-BUTT is not 244-2888 but 11-18-16-11-30-29-29 and would be dialed 02-#4-*4-02-08-*8-*8. Though technically one is required to *press* more than (say) 7 buttons (without going to 36-key pads!), the actual _code_ is only 7 "digits" long.

Unlike [Dignan]'s idea, this would give over 64 BILLION (thousand million for you Brits) standard 7-digit codes. Note that some cities use 10-digit dialing now - this would give almost 4 quadrillion numbers, or more than half a million for each person on the planet! The large number of possible combinations would also allow us to dispense with the international and area code systems in use today, at least for a few more generations....

I confess that the 7 and 9 keys (which have 4 letters each) might pose a problem, but if we're prepared to revamp the world phone system, we can certainly rearrange the letters on the keypad a little bit, eg. by moving two letters onto the "1" key.