The absolute minimum for a domestic flight is 30 minutes. This means that if you're not checked in 30 minutes before departure time, you will be denied boarding
At major airports this limit is extended to 45 minutes. After this limit you will not be allowed to check bags and you'll be denied boarding
some airlines will extend this to 60 minutes. So you need to check on the airline's website.
Note that these are the "limits" so you need to make sure that you have enough time to get checked in. And often, the closer to the "cut off" time, the bigger the crowd at check in.
I would not dare to come in later than twice the time limit (90 to 120 minutes)
For international flights, that's 3 hours