Is "warm" a compliment or a criticism?

I have noticed that when some people describe the sound of equipment as "warm," they mean it in a positive way, while others seem to equate a warm sound with muddiness or lack of detail. What exactly does "warm" mean?

Too much of anything is always a bad thing. If something is too warm, most anyone won't like it. Personally, I like a warmer sound. But, that's just me. Depends on what type of sound you like. I usually take it as a compliment.
I agree. It's all a matter of perspective.

I like women with curves, but I know some guys that like women with "boyish" figures. I don't get that at all, but to each his own.
Isn't "hot" better than "warm"?
In theory, the objective of high-end audio is to reproduce the sound on a recording as accurately as possible. Hence, if the recording has a "warm" quality, that is what should be reproduced by a good system. Likewise, if a recording has a rather cool or analytical quality, that's what should be heard.

People being human, however, there are different "tastes" in reproduced sound. Some folks really like detailed, analytical sound (which, to my ear, often does not sound realistic), while others want to feel enveloped by warm, inviting sound. These preferences for sound quality used to be associated with the "solid state" camp versus the "tube" camp, but the best high-end audio gear today offers the best of both. I think that the term "warm" is used today to suggest the kind of sound that has some emphasis on the upper bass and mid-range, which is the portion of the audible sound spectrum where the human ear is the most sensitive (and, not so coincidentally, the range of the human voice).
I always think of it in terms of temperature, because music is a lot about how it makes you feel: Cold and lifeless, cool and distant, warm and sluggish, hot and irritating; yet, it can also be cool and collected or warm and inviting etc. There's a fine line between the different temperatures/descriptions and I think one thing to keep in mind is that the opposite of warm is not cold but cool. Since our own temperature fluctuates, what is warm one day can seem cool the next and viceversa. So that's another reason to seek a neutral balance (I don't care too much about reproducing what is exactly on the record). I usually prefer my drums to be relatively hot and electronic instruments to be relatively cold, but woodwinds have to be warm (if not either the player sucks, the recording sucks, or my system sucks :P). But this comes naturally. That to me is the whole point of being accurate. You have to screw up to make a warm sounding instrument sound cold.
'Warm' is inherently neither good nor bad. It descrobes a tonal balance that has more energy in the lower half--say, below 500Hz--than in the upper half. (A tonal balance having more high-frequency energy is called 'bright'.)

Warmth is absolutely a coloration, an error, but usually it sounds wonderful if not overdone. But warm becomes 'thick' rather soon.

So whether 'warm' is good or bad is truly a matter of opinion, but WHAT it is is rather commonly accepted.
Better "warm" than "cold". Better slightly "warm" than hard, steely, over-detailed with pinpoint imaging, tiring over extended periods, etc.

Gunbei is right.

Curves=good. Skinny straight stick chick= need sandwich.

For audio equipment, I've frequently heard tubes described as yielding a "warm" or "full" sound. When I listen to my Cary SLI-80 Signature driving my Revels however, I don't notice "warm" so much as "rounded yet detailed".

I think the term "warm" can be interpreted as good or bad- as you stated. So for audio, it's probably a fairly ambiguous and poor term.
At the least, "warm" means that the sound is not shrill or harsh. Most anyone would consider that great news. But beyond that, the meaning seems to depend on writer / speaker and the situation. A system that portrays the beauty of midrange, such as female singer or sax, can be described as warm. But "overly warm" suggests that details are being sacrificed in exchange for presentation of a sound that is pleasant, but lacking in realism.

For many years, it seemed that most transistor gear had a harshness or graininess to it, and so "warm" was a welcome relief from this problem. Todays best systems seem to sound realistic without being either grainy or overly rich or colored ("warm"), and hence this term can had positive or negative connotations.
One man's ceiling is another man's floor-Paul Simon
While Jeffreybehr makes a valid point regarding a possible hump in the FR between 100-300Hz (that could be even "lumpy" for some people) or alternatively a notch in the 2-6kHz region, IME the term "warm" is usually used in a positive vein:
the sound is full "enough" -- i.e. there's sufficient energy but not more than necessary -- in that region.

Mind you, one person's "warm" could be the next person's "lumpy" ESPECIALLY relative to the spl at which this comment is being made: at low spl our ears are less sensitive at 100Hz than they are at 3kHz!
It's usually neither. It is more like a benchmark as with dead neutral as the center. Krell preamps have had the reputation as being stark, cool, tremendous base slam. Where the top end Classe preamp, has been descriped as warm, rounded,laid back similar to Rowland equipment. None of the aforementioned descriptions are positive or negative, just a positioning on the neutral continum. It does turn into a negative when a Reviewer states that the sound was too cool or too warm. As in most things who is to say what is dead neutral. Everyone has their own perspective of what a system is supposed to sound like. Whether your system is yin or yang, if your tapping your feet to the music, who cares.
Gunbei, Are you having a Wierd Science kinda day? All your posts are Female Part's related? Feet, Curves, Etc... Could get somewhat Warm if your sitting in front of your computer with a Wonder-Bra on your head, designing the Perfect Woman.
Audiobugged, actually your picture of me is a lot closer to the mark than you think. It's what I do for a living. Sans the bra on my head. Heheh.
It is possible it arrives only as an observation, a way to discern a components contribution to a systems overall sound. I have viewed it both ways. Rigid thinking has me rejecting colorations of any kind, and for that I am a bit at odds with my system. Ideally, I want the recording as is.That is ideal. Yet, I imagine that I can really only imagine what that means. In reality, it seems the warm sound resulting from the choices I have made for my system makes for a friendlier listen and this is ultimately my preference. All of it and warmth, and then everything my way.
Gunbei, ever heard the term "boyish but sexy"?
Psychicanimal, no I haven't heard that one.

But the gay guys I work with talk about "sexy boys''.

The only difference is that they remove the "butt" from their phrase, which to me is a bit surprising.