Would a ‘Last Will and Testament’ posted here on the SDMB be regarded as a legal will, for all relevent intents and purposes?
Hmm no signature, no witnesses to the signing, no proof as to who wrote it even if it came from your computer. On the other hand there can be oral wills but they still have witnesses.
Mutant is right. Short of any actual evidence that it comes from the testator, it shouldn’t work.
A few thoughts.
Some states allow holistic wills, in the handwriting and signed by the testator. If a state had a law that electronic sigs were just as good as written sigs, would that work?
The witnesses must by physically in the room with the testator. If the testator was using Skyppe, or some other live program and there were the required witnesses at the same time on their computers with him, would that work? Probably not.
Yeah, after I typed my post it occurred to me that you could have witnesses but you would still have the signature problem. Not just the signature of the testator but also the signatures of the witnesses.
Not in my jurisdiction.
For people who are interested in this, it’s called a holographic will. In states where they are legal, I believe they are as good as a formal witnessed will. The only downside I can think of offhand is that they will not be valid as to the disposal of property located in a state that does not recognize them. Also, it used to be that they were not valid as to real property, but only personal property, however I’m not sure that’s accurate and even if so, it may not still be true.
Also, although rules vary and you will need to do your own research or talk to a lawyer, I think the will has to be COMPLETELY in the handwriting of the testator - not just parts of it and definitely not just the signature.
Are you leaving me your post count? 
Yeah, in law school we heard the very sad case of the schmuck who bought one of those pre-printed fill-in-the-blank “Last Will and Testament” forms, filled it out, then died, probably thinking he’d got himself a will. But because the entire will wasn’t handwritten, it didn’t qualify as holographic, and because it wasn’t witnessed it didn’t meet the regular standards. At least the guy was already dead…
What happened to all his stuff?
It would have passed via the law of intestate succession. Intestate just means you died without having a valid will. In that case, the law in the state where you reside determines what happens to your estate (although property situated in other jurisdictions may pass via those states laws - not sure about that part).
Normally, immediate family will become the de facto heirs to the estate. Sometime this means a spouse, children, siblings or possibly even some combination of those. If there are no surviving family members, then there is a laundry list of people and entities who may be eligible to inherit. That too varies from state to state.
If you go down the list and exhaust all possibilities in terms of potential heirs, then the money escheats to the state.