How long before the flight can you check in??

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I was wondering if my flight leaves at some early morning ungodly hour then can I check in on the previous day? How many hours in advance can I do this on international sectors for flights originating out of the US? Is there also some operational upgrade list like on United based on the "first come, first get it" basis?
I was wondering about this as well. Last year in Vegas, I had a flight returning to IAH at 7pm, of course I had to check-out the hotel by noon, I wondered about check-in but did not do it...

I don't know about American, but on Alaska/Horizon, I believe it is 4 hours before flight time.

Last year, I was doing a segment run to take advantage of the AS/AA promotion. I had scheduled PDX-SEA-PDX-SJC, and on check-in at PDX, I asked if I could just check my luggage for the final PDX-SJC segment. The agent looked at the schedule and allowed it because that segment was less than 4 hours away.

And afang, in case you weren't aware, at almost all hotels you can ask the bell captain to store your luggage for you until you're ready leave. I've often had situations where I check out in the morning, store my baggage at the hotel while I'm at my business meeting, then collect it when I'm ready to head to the airport. No charge, as such, but I always give a tip.
I'm pretty sure on all the major US carriers it's 4 hours prior to departure of the first/next segment -- at least for domestic flights.
On AA, the airport takes control of the records 4 hours before flight time and hence, you can only check-in 4 hours prior. THat being said, LGA used to offer midlight check-in -- they would check your bags in the night before your flight. I am not sure if they are still doing it or not.

--Jim
I think that AA has changed the rule to 12 hours. I was just at PDX and wanted do some changes the night before. The agent looked at her watch at told me that if I waited for a few minutes I would be in the 12 hour window to check in.
I think it's at least 12 hours. Not sure if there's a distinction between domestic and international flights, though. This past Friday morning, I checked in for both my MEX-MIA (11:50am CST) and MIA-GIG (11:30pm EST) flights at about 10:30am CST. I received boarding passes for both, and my luggage was tagged/checked through to Rio de Janeiro, so I didn't have to claim it in Miami and take it through customs...