Ok, for the most part I think you've convinced me. There simply isn't an explicit rule that says death from negative levels (that are gained separately from an energy drain effect) would do anything but simply kill you. Both the FAQ answer about unholy weapons and the SRD description of the
enervation spell (which also gives neg levels without mentioning "energy drain") say it can kill you, but mention nothing about rising again as a wight. And you'd think that would be a fairly significant point to mention.

So I guess negative levels by themselves can kill you, but not make you a wight.
Now with the point conceded, I do still have some questions/comments on a few of your responses- but only to clear things up and avoid confusion.
Why? Only the FAQ answer leads to that conclusion.
Are you saying that a 1st level good character picking up an unholy weapon
would not be killed as a result of the negative level gained? I'll admit that he won't become a wight because of it (although I think it's cooler if he does- it makes such weapons much more evil if they can create an evil creature that can then wield it in combat.) but I'm pretty sure the negative level will kill the character. Every source mentioned in this thread that talks about negative levels all agree that when you get as many as you have character levels- you die. I agree now that you don't necessarily become undead afterward- but you are slain.
Spells can cause energy drains (which a warforged is specifically immune to) but the animate dead spell (a necromancy spell) with a target of 1 corpse {no type mentioned} should work since it has nothing to do with energy drain.
Actually
animate dead won't work because of the template problem. This is mentioned at the end of the faq entry you quoted. The spell might be able to target any corpse but it's effect is a templated creature. Both the skeleton and zombie templates require a corporeal creature with a skeletal system. If you go with the faq answer, which states they don't have a skeleton, then they can't be animated as either undead. If you ignore the faq and rule that they do have skeletons, then they can be animated by the spell.
As far as gaining negative levels from an unholy weapon...
There is a difference between being dead and becoming an undead from the effect.
Point conceded.
Just one last thing for my own clarification, because I try not to argue sloppily...
...taking the section of text about being dead from negative levels out of the context is in general bad form. The text (in the DMG) is written in conjunction with energy drain and not something that stands alone.
What was I taking out of context? I tried to only talk about the negative energy definition from the online glossary. And I don't think that was out of context. I mentioned only the glossary entry specifically because it was not in context with energy drain. Or are you talking about the being dead from negative levels in regards to the faq answer about unholy weapons? If so, then yes I think I was wrong about what it would do (bring you back as a wight) because of the glossary entry. I combined the death-by-negative-levels bit (in the unholy weapon faq) with the rise-as-a-wight result (from the glossary). I don't think that was out of context (although I do now think I was wrong) but I could have been more clear with regards to the connection I was inferring between the two sources.
Anyway, to sum up...
1) More neg levels that character levels = death (and nothing more)
2) Too many neg levels again, but his time from undead energy drain = death then rising as that type undead, or a wight
3) 1st level good guy vs. unholy weapon = dead good guy, but not undead non-good guy (although it's cooler if they do become undead)
and finally,
4) Without spells that strip away the living construct type, the only RAW undead that work on warforged are Spawn of Kyuss- provided one rules that warforged have a brain which can be burrowed into by the spawn worms. According to the faq (for whatever that's worth) they do have brains- see question on page six about having said brains extracted by mind flayers.
Actually, as a complete aside from the whole undead business, the entire warforged section of the faq is a rather haphazard, bizarre and somewhat contradictory explanation of warforged "biology." From the various questions it is inferred that warforged...
...are only slightly denser than other races and can swim with only mild difficulty.
...don't need to breathe but are vulnerable to depth pressure.
...are immune to fatigue and exhaustion, but still take non-lethal damage from overworking themselves (running, forced march, etc.).
...do not gain adamantine slam attacks even if they have the adamantine body feat.
...have a brain (edible by mind flayers no less) but no skeletal system.

Curiouser and curiouser.