This question is a perennial one on the Planescape Mailing List, and one which strikes at the heart of the Celestial culture. I've divided the point up into a number of sub-questions, so read on.

Do Celestials fight at all?

Certainly they do. That's clear from the descriptions of creatures like agathinon and solars in the Planescape Monstrous Compendium Appendices. They don't necessarily enjoy it, being the good guys, but they are willing to fight against evil, for example.

Do Celestials fight non-evil entities?

Yes. They consider this even less fun than fighting fiends, although archons have little patience with slaad, and eladrin loathe modrons. They will fight such creatures as it suits their aims. For example, if slaadi come rampaging into Bytopia, the archons (and indeed the guardinals) will come down like avenging angels (fair enough) to kick them out again. They won't, on the other hand, take the fight to the creatures' home planes without excellent reasons.

Do Celestials fight each other?

Yes. On page four of the Planescape Monstrous Compendium Appendix One, under 'Warriors', it describes how the agathinons are pawns in huge wars between pantheons over ideological and territorial disputes. However, it's important to note that these wars are not fought in the name of Good, but in the name of Zeus, Odin, Moradin, and the other gods.

Are Law and Chaos fundamentally opposed?

They seem to be. The Xaoticians might argue otherwise, but it seems almost axiomatic to the Planescape setting that the two should be on opposite sides. Note that, unlike the situation in Warhammer, Basic D&D, and, to an extent, Fighting Fantasy, Chaos is not equated with Evil or Law with Good in Planescape.

Is the Blood War about Law and Chaos?

To an extent. Certainly the more ideologically minded fiends on each side picture themselves as champions of their chosen alignment. But the basis of the Blood War is simply genocidal hatred. It's what characterises fiends. Fiends are, of course, from a design point of view the epitome of Evil, and genocide is widely considered to be amongst the most heinous of crimes. Naturally fiends should be all for it. And just so nobody supposes that all fiends of one alignment are allies, don't forget that baatezu and rakshasas, yugoloths and gehreleths, and all kinds of tanar'ri, all fight one another.

Do the Celestials, therefore, also fight over Law and Chaos?

No. No such war has ever been suggested in any Planescape resource. The Celestials, as the epitome of Good, are fundamentally opposed to the idea of unrelenting genocidal war. Some people on the Mailing List doubted this point, stating that there was as much a gulf between archon and eladrin as between guardial and yugoloth or baatezu and tanar'ri. That's true. But because they're good, the Celestials try to resolve issues by discussion rather than by armed conflict. Every now and then there's a duel, or a short clash of celestial soldiers, but by and large the Upper Planes are peaceful. I asked the Planescape designers what they thought about this issue, and I was pleased to have my own intuitive answer backed up. Here's what they said:

I have to disagree wholeheartedly with the notion that the celestials make war on each other as fervently as the fiends do. The very nature of goodness dictates a view of the sanctity of life, and to waste lives fighting over the definition of goodness is a paradox. Though I'm certain that small, bloody, and ferocious conflicts occasionally break out among the more idealistic and uneducated of the celestials, it's my guess that these warriors, unless they make their war under the direct command of a god, are severely chastened and perhaps cast down from their lofty perches by their fellows.

Good exists to promote goodness. Slaying other champions of goodness when there's so much evil is both counterproductive and foolish, and definitely borders on evil.

Yes, belief is power, especially in the planes. But I think the celestials would, for the most part, be wise enough to realize that their slaughter of each other serves only to increase the power of evil.

Intermittent holy wars, I can see, especially under the command of gods. A full-fledged Light version of the Blood War would be out of the question. Any such struggle would be waged by philosophers, diplomats, and, in rare cases, single combat to promote an idea.

- Colin McComb

As for a celestial Blood War, I just can't see it. There might be occasional, brief conflict, but not actually a war. It just isn't, well, good.

- Monte Cook

... [T]here is no Blood War-type battle going on between the celestials of the Upper Planes. I'm not saying that things are completely peaceful - there's always that law/chaos split causing tension - but they're not killing each other.

- Ray Vallese

Thanks, guys.