Science reveals how not to spill your coffee while walking
nbcnews.com
nbcnews.com
Having been a cafe server for 4 years I can say from experience that you can practically run with a cup of coffee without spilling it. Several times a day I would pour a cup of coffee while I brought it to a table - often without constantly looking at it, my eyes were always scanning tables.
That said - if you take enough steps with a full cup of coffee it will eventually spill, that's something that us wait staff actually talked about. We rarely spilled coffee.