I've heard people being able to use it on entirely different machines after phoning up Microsoft and telling them the old computer stopped working and they got a new one.
No - what you have heard is people not telling the truth when they contact Microsoft to activate their product.
What you can legally do and what you can physically do are two entirely different things.
If you call MS for activation of an OEM OS, tell them you've moved it onto another machine they will tell you no, you need a new license.
Even if your old machine totally stopped working, unless the new machine is a warranty replacement (and if it is it's likely to have a new copy of Windows on anyway) it doesn't matter.
If however I call up MS afetr moving my OEM copy of Windows from one machine to another and I tell them it is due to a HD failure or motherboard warranty swap then they will most likely activate the OS over the phone.
However what you need to realise is that in this situation you are no more legally licensed for your OS than somebody who downloaded an illegal copy from the net.
You need to decide if you want to be legal or not when it comes to MS licenses.
There is no "middle ground" or "grey areas" - you are either licensed or you are not.
If you plan on being legal then buy your OEM license but be prepared to buy a new one come motherboard upgrade time.
If you aren't prepared to do this then really why bother even buying the first OEM copy?
You only remain legal until your first MS swap - so really there is no point buying even your first copy.
You need to decide if you plan on joining the real world where people have to pay for what they use or if you're just going to freeload.
Vista is expensive.