The carry-on rules on any of the airlines that I fly allow "one carry-on one bag and one personal item." The carry-on bag can be a limited-size suitcase, such as the 20" rolling bag. The personal item can be a computer bag, purse (male or female, as the airlines are quick to point out), briefcase, or similar sized item.
If you feel like juggling more objects as you board the plane... such things as a coat or a McDonald's carry-out bag don't count against your carry-on allowance.
Offically, a medical device, such as a CPAP, doesn't count against your carry-on allowance either (as long as it's within the size limits) -- but that doesn't mean that all security, TSA, and airline employees know this rule. I've had to ask for a supervisor several times as over-zealous employees refused to look at the printout of TSA and airline rules that I carry with me for such cases.