UDID

UDID is short for Unique Device Identifier. It is a 40-character long hex value (20 bytes). You can easily find out a device's UDID in iTunes, when the device is connected, by clicking on Serial Number.

You might hear about UDIDs because developers registered with Apple can list up to 100 unique devices that can test their apps, and they list these permitted devices by listing their UDIDs.

Calculation
The UDID is being calculated like this:
 * Create a 60-character long or 59-character long (on newer devices) text string (see below)
 * Calculate the SHA1 hash of the text string. The result is the UDID.

To create the text string, append the following four strings:
 * 11-character long or 12-character long (on newer devices) serial number (exactly like it is written in the Settings app)
 * one of these:
 * (on older devices) 15-character long IMEI number (without spaces); empty string for iPod touch and Wi-Fi model iPads
 * (on newer devices) 13-character long ECID in decimal, no leading zeroes
 * 17-character long Wi-Fi MAC address (letters in lower case, including colons); for the iPod touch first generation use "00:00:00:00:00:00"
 * 17-character long Bluetooth MAC address (letters in lower case, including colons)

In short
On the Verizon iPhone 4 and newer: UDID = SHA1(serial + ECID + wifiMac + bluetoothMac)

All else: UDID = SHA1(serial + IMEI + wifiMac + bluetoothMac)

Changing UDID
The UDID can be changed by running the command below, followed by a DFU restore. If the DFU restore is not performed, many applications will break, including iTunes. It is very important to first write down the original MAC address and keep that information in a safe place so that you can revert this change if necessary. This hack is shown on an iPod touch 4G.

It is also very important to not change this to an invalid MAC address. If you change your device's MAC address to something invalid, your internet won't work again until you fix the MAC address (using MobileTerminal or similar). This persists even if you restore -- so you can make this really really hard to fix (you can call it a form of bricking) if you restore and there's no jailbreak available, if the available jailbreaks don't include afc2 and other workarounds aren't working.

Note that changing your UDID can have weird side effects in general, including that you'll have to log in again to everything, including Apple apps.

If you're still willing to risk this, this is the command:

nvram wifiaddr=ma:ca:dd:re:as