I always thought it was something of a joke, used in comedy skits or all-men productions where there are female parts.
Is it actually a valid/serious singing style? Not to be confused with your normal 'head voice'.
Sure. I think the majority of countertenors employ falsetto for considerable parts of their range. Check out Ombra mai fu in the version of Jochen Kowalski, a countertenor mainly employing falsetto. That's certainly a valid/serious singing style. His hallmark role indeed is "Prinz Orlofsky" from the operette "Die Fledermaus" which is a comical role, and usually assigned as a "trousers role" to a female mezzosoprano.
Lots of baroque operas were written for castrati (the popstars of that era, but it's not like we did not have flamboyant alto range singers like Michael Jackson or Prince as well), and a reasonably stylish performance these days requires skilled countertenors, often falsettists, to navigate the range convincingly.
Perfectly valid in modern styles too.
As user15575 mentioned, Prince & Michael Jackson were famous exponents of it.
I recall this example from the 80's - though not as polished as some of the more famous examples, the singer in this (Jimmy Somerville) stays in falsetto for the entirety of the song, even down to his lowest notes.
There is also the far more famous
which I haven't heard in years, but just realised again how good it actually is (& I can't stand disco usually)