Cheap PSU's tend to not give enough stable power when you pc needs it......
you might be doing something that makes you cpu hit 70% or higher and your processes might crash out or pc blue screens/locks up.
and I have seen cheaps psu go pop (loud bang and sparks shoot out of psu) when you graphics card is under load.
But I myself have not seen a cheap damage any other pc components. most modern components have some sort of surge protection, that older parts might not have.
I tend to recommend name brand psu's for these reasons. and you can get good coolermaster and evga psu's pretty cheaply.