This really boils down to a matter of opinion, based on the type of instrument you are amplifying, as well as your personal preference for sound. Tube and solid state produce a different effect. Let's explore these amplifiers shall we?
Image source: http://photobucket.com/gallery/user/StuartC_01/media/cGF0aDovX1NNQzMyNTcuanBn/?ref=
Tube amplifiers are commonly associated with "classic' amps. Their use became popularized in the 60's British Invasion of Arts.
Artists such as Jimi Hendrix, Stevie Ray Vaughan, The Beatles, Led Zeppelin, and many many more used this type of amplification, and recorded their musing using analog equipment, which vary's in contrast, quite different to the digitally produced music today!
Solid state amps produce a tone that is more suitable for digital recording, and is less "natural" it's feel, but this doesn't mean less desirable! Some genre's of music call for a solid state feel, and the tube's in tube amplifier's cannot handle some of the effects produced with modern effects processors!
Some bands that use solid state amps today are: Meshuggah , Korn, slipknot, Weezer, Metallica, and the list goes on and on. They are very popular for use in today's application.
I personally prefer the nice warm tone a tube amp produces, although for some genre's I prefer a solid state! This is generally the case when I play metal, but if I am playing classic blues rock, I prefer a tube amplifier.
I hope this answer helps! Thank you for the thought provoking question!