I agree with Arravis in part--people should be killed for their actions not for their alignment. Many evil people do not deserve death from human (or demihuman) institutions--indeed, human and demihuman institutions are set up and continue to function to a large part because they manage to control the evil people who are a part of them and keep their evil from manifesting in ways that create more harm than killing the evil people would create.
However, I agree with LuYang and Wizardru in part. The man who intends to do evil and would really follow through with it if given the opportunity is evil whether or not the opportunity presents itself. Now, it's clear that, if the opportunity never presents itself, we will never know, absent omniscience, whether the individual would or would not have followed through with it. We don't know whether the man is losing the battle with his demons but hasn't lost yet or whether he's entirely surrendered. However, I don't think it's much of a stretch to suppose that there is a difference between the conflicted individual who will do evil and the conflicted individual who plans to do evil but won't follow through--before the opportunity to do evil is past. Nor do I think it's much of a stretch to believe that Detect Evil can tell the difference between the two.
(Of course, that's not the same thing as saying that the evil detected would be worthy of death. The man who struggles with his conscience and can't bring himself to kill his landlady may very well detect evil because he has no problem embezzling the money he collects for orphans (which is generally not thought to be worthy of death these days (although it would have been in some days past)).
However, there seems to be a rather pernicious notion going through this thread that a paladin would never kill a neutral or good NPC. I don't think that's so. There are plenty of justifiable reasons for killing that could apply to a neutral or good NPC just like the justifiable reasons for killing don't necessarily apply to an evil NPC. For instance, a paladin who is on the righteous crusade to destroy the wicked hobgoblin empire of Naziesqueness may well find that he is facing neutral or even good soldiers on the other side. Perhaps they were conscripted or perhaps they see it as their duty to defend their homeland. Perhaps they are honoring an oath or perhaps they just don't want to see their farms destroyed and their families without food (common consequences of losing a war). Whatever their reasons, I don't think that their lack of corruption or even goodness means that even a paladin would be obliged to put up his sword. (He might well want to and try to negotiate but they have good reasons for not listening to him. If they are both wise and good, they probably both appreciate the tragedy of the battle but participate in it anyway).
If a neutral Meepo were to side with his people against the Paladin, it would not be necessary (and perhaps would not even be advisable) for the paladin to deal subdual to Meepo. The question would not be whether or not the paladin killed a neutral kobold but whether or not the paladins attack on the kobold tribe was justified.
Incidentally, since a lot of this is being blamed on the D&D alignment system and Detect Evil in general (one poster even favorably referring to the 2e "only real EEEVEEIL" (or immediate eeeveeeil intent) version of detect evil), I think I ought to say a few words in its defense (or at least in contradiction to the ridiculous idea that the 2e version was more conducive to a game that explores moral dilemmas). The idea of detecting evil is only foreign to those to whom the very idea of evil is foreign and passe. IRL, those of us who believe in evil may have less sophisticated methods of detecting evil (relying upon witnesses and making decisions) but we none-the-less come to a lot of definite conclusions about what (and who) is evil and what isn't. (Even those who claim that they don't believe in such simple-minded concepts as evil come to such conclusions if the vituperation about Ashcroft and Bush is to be taken as evidence of what its speakers actually believe). For most people, the challenge is distinguishing between degrees of evil and discerning the correct reactions to it. The challenge for the D&D paladin doesn't become any different from that just because he can eyeball the broad categories of evil/not quite evil or actually good.
In contrast, the 2e "EEEVEEEIL only" interpretation of Detect Evil is actually much more suited to a black and white game where the proper response to Evil is always to kill it. When Detect Evil doesn't detect Scrooge, or a serial womanizer, but only fiends in human form and their high priests, it really IS a license to kill. (Certainly there are still people who don't detect as evil who the paladin is justified in killing also but at least one class of people (those who detect as evil) are unambiguously marked for death). That is not the case in a system where pickpockets, sharpers, and fiends (well, at least weak ones) could all respond to detect evil in the same way.