Chris, its on-topic as far as a signature sound is concerned, on account of the fact that tube amps use far less feedback or maybe none at all compared to transistors. I am referring to global or loop feedback.
Local feedback can refer to loop feedback around a single stage, which can still be problematic, or it can refer to degenerative feedback, which does not involve looping around a gain stage and so does not cause trouble.
The ills of loop feedback have to do with a phenomena of all amplifiers called propagation delay. This is the time it takes for a signal to propagate from the input to the output of an amplifier or from the input of a gain stage to the output. The delay is a constant for a given amp and does not change with frequency. From this it might be easier to understand that a loop feedback signal will never arrive back to the input in time to correct the signal that it is supposed to.
As frequency increases, so do problems caused by the lateness of the feedback signal. Eventually this can cause the amplifier to oscillate, so wide bandwidth amplifiers usually have a mechanism to reduce feedback above a certain frequency where oscillation might be possible.
Anyway, negative feedback is a *destabilizing* factor in an amplifier, but will improve overall distortion and sometimes increase bandwidth, at a price: it will, while decreasing most distortions, actually *increase* certain odd ordered harmonics, not much (actually we are talking hundredths of a percent here), but enough so that the overall effect is as MrT describes above as a perception of brightness. You might get with it more detail (as getting rid of distortion reveals detail underneath), but the amplifier may be painful to listen to.
My own opinion is that feedback has to be avoided if you are to have an amplifier that will lack loudness/harshness cues. You still want to get detail, so you still have to reduce distortion- you do this by using linear amplification devices and techniques, so distortion creation is minimized. A couple of examples are triodes and class A operation. Of course, I think a major contributor is the output transformer :)