Subject: United Carry-on
United's web site says: Carry-on baggage is limited to one bag and one personal item. If you are checking or carrying baggage, find out more about free baggage allowance and size and weight limits.

Here's the url: http://www.ual.com/site/primary/0,10017,1031,00.html

I noticed that on my last UAL flight (two weeks ago) they were extremely strict about this.

Joli Wilson San Rafael, CA