(At) home

It's a well-known fact that home has no preposition when it occurs with go:

I went (*to) home

(The asterisk inside the brackets means that it's ungrammatical if you include to.)

And it has to have one if it's an adverbial phrase (optional extra information about the event):

I worked *(at) home today

(The asterisk outside the brackets means it's ungrammatical without at.)

There are some verbs where the preposition is optional, such as stay:

I stayed (at) home.

I think there might be some regional variation on that one, though I'm not sure.

But when it's with be, omitting or including the preposition gives a meaning difference. I ran a twitter poll to make sure I wasn't alone in this, and found overwhelming agreement with my judgements. In a context in which I've been for a night out and want to tell my friend that I've arrived back at my house safely, I would say I'm home. If my friend had rung my and wanted to know where I was, I would say I'm at home. I could use either in either context, but both I and those who responded to my twitter poll felt that the distinction above was right. So that preposition at being pronounced has a kind of locative meaning - location in a place - while omitting it has some sort of directional meaning - movement to (or arrival at) a place.