Illegal copies are as old as the copyright laws that give the originators of new work the exclusive right to copy and sell that work for a limited number of years. Illegal copies are made of computer software, music, movies, and even books (if you scan or photocopy whole chapters).
In 20 years I've seen everything tried: Software that can only be loaded once. Software that checks for a piece of hardware attached. Software that is tightly restricted. And software that is not restricted.
What Microsoft does now is issue with each disk a physical index-card-sized Certificat-of-Authenticity or COA. The COA is your proof of purchase, and if the sheriff visits your company with a warrant, your company should have a COA for each machine running a Microsoft product. In addition to the COA, there is often a 1.5" by 3" sticker attached to the computer, making the 1:1 match of macine-to-software easier. The new XP technique of authorizing software by requiring legal keys to be registered is a helpful adjunct, but as I understand, it is the possession of a COA in 1:1 correspondence between machines and installations that is the controlling factor.
On 1: One thing not mentioned above is MS pricing, often 5 to 20 times more than their competitors. People feel "justified" in literally stealling the MS products, because they perceive MS illegally extorting from them.
2: I think the introductory comments address that.
3: It is not that MS leaked the formula for creating keys, as somebody was able to conceive a formula that produced keys, but not necessarilly all keys. There are few people who get deep satisfaction in out-thinking the big-guy, or solving the insolvable problem. But, in combination with those masses willing to exploit the solution, you will probably always see a race between those who try to stop illegal copying, and those who practice illegal copying.