"I'm home" or "I'm at home"

Solution 1:

• "I'm home" is what you say when you walk in through the door to tell people there that you've arrived.

• "I'm at home" is what you say when someone asks you on your cell phone or IM (Instant Messenger) where you are located: "Where are you?" "I'm at home right now."

Solution 2:

I think the implication in the expression "I'm home" is that you're home from somewhere. It may, as Mitch says, be that you've just come/gone in, but it doesn't need to be — you can be home from the front or home from university and have been back for a week or so. But a homecoming in the not-too-distant past is certainly connoted.

The nature of the word home in "come/go home" is often argued over; noun and adverb are suggestions, but directional particle is what I'm voting for at the moment. Apparently, home in go home can be used without a preposition because it is the remnant of an earlier form that fused preposition (to) and noun, and when this type of inflection for case disappeared from English, this particular usage continued, with the to-home form standardising with the base noun. We don't have "I'm going school". Possibly, "He is home" has arrived via "He has/is come to-home". Home in "He is home" is locative rather than directional now.

It may be another legacy from the fused to-home that we never use the preposition to with home (except with an intervening determiner etc.), but this is true for other nouns also.

Certainly, other prepositions (at, from) can be used with the noun home in the expected way, and "I'm at home" is strictly locative. To express arrivals at other venues, we are forced to use a different expression — "I've just got to school / I've arrived at school", as psmears says.