what makes a tube sound the way it does?

Tubes overload easily. Tubes sound nice in overload. They act like a compressor. They add lots of the right kinds of harmonic distortion during overload and this can make a pleasing sound. It can even make the music more audible to our ears/brain ( we are very susceptible to discerning harmonics)

Solid state can be more robust and play at much higher levels with better linearity = more accurate. However, when Solid State clips it sounds awful and immediately becomes much less accurate.

To get good sound with Solid State you need to absolutely ensure no clipping. (i.e. requires a very powerful amplifier and an easy load). A good linear tube amp will actually sound almost identical to solid state up until the point it clips (often this occurs at very modest levels due to transient peaks) at which point it gives that famous "tube sound".

Tubes are used a lot in recording studios for miking and also for mastering....that pleasing tube sound can improve a "thin" sounding mix...it can also act as a limiter to reduce dynamic range on a studio mix in a very elegant way. Studio miking with solid state can prove to be a challenge due to the shear dynamic range involved...as already mentioned a tube amp recording a mike will clip nicely if the sound goes out of range whilst a SS amp will sound awful as it clips....so tube amps offer advantages if you don't get the gains correct or the mike is placed too close to the instrument.

Here is some reading material, enjoy......

http://home.comcast.net/~enghenry/diy/taste.pdf

http://werple.net.au/~gnb/elec/valvedata.html

http://www.theabsolutesound.com/newsletter/147/tubes_vs_trans.html
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OTL (Output Transistor-Less)

There are scientific reasons tube based equipment will sound different to the human ear. First, a tube plays about 4 times louder per watt than solid state. A tube's harmonic distortion occurs on an even order as opposed to solid state devices where it occurs on an odd order. And yes, when tubes approach clipping, they are more "rolled off" than solid state equipment. Also remember that with tube equipment, one can use different brands and types of tubes which can affect sound quality. If you are considering a "single ended" tube amp as opposed to a "push-pull" type tube amp, you will want to consider a high efficiency speaker. Like with anything else, there are good and bad tube based equipment. Look for a well established manufacturer. There are a lot of "garage" made equipment that probably should be avoided.