I searched for Verizon and USB but couldn't find anything about this...

My PSP, GPS, Blackberries, phones, headsets, PS3 controllers, external hard drives, etc, all use the same mini usb plug, but the Blackberries from Verizon use a different interface.

I have over 100 of these universal cables, which I use for everything, but if I switch from ATT to Verizon I'll have to carry another cable with me just to satisfy this new standard.

Why is that? Is there a technical reason for it?

Depends which Verizon BlackBerry device you are referring to.
They all used mini-USB up until the Storm (9530) was released.
Starting with the 9530, RIM switched to Micro-USB, as it is becoming the new standard.

It's not a Verizon thing... it's a RIM thing.

If you want to use your current mini-USB cables, then either get an adapter to make them micro-USB, or get a Verizon BlackBerry that has a mini-USB port instead of a micro-USB port.

microUSB is the current mobile phone standard. RIM is merely making devices with it. My Verizon MiFi uses microUSB. New BlackBerrys have been using microUSB for a year now.

There are very inexpensive converters available (and LOTS of threads on this) - Motorola part number SKN6252.

A sign of the times. This is one time that we can't blame Verizon for this ...

I don't think mini USB was ever really decided upon as a standard for mobiles. However, I think there is a push to standardize on micro USB.

First Google hit I ran across:
Universal cell phone chargers coming soon | 3GSM blog - CNET Reviews

Pick up a couple of These adapters from Amazon. I use one with my BlackBerry Tour. Just plug the older mini-USB into one end and the cable becomes the new micro-USB type.

Most of our new phones have the Micro USB cable port.
It is supposed to hold up to a larger number of plug/unplug cycles, and seems much more solid.
I have bought a bunch of cables and adapters on ebay. Most are shipped from China, but work great.