The typical rank and file soldier, no. Officers, yes. But what they did carry depended on what they were doing. In most places the typical private would carry his service rifle around with him wherever he went. As the war progressed and tactics developed, men within a platoon would be dedicated specific roles/tasks for an action [eg. assault, raid, etc] and would carry particular tools to fulfil that task [eg. one man might carry bombs, another an entrenching tool, etc]. See this great image of a platoon of Australians about to go into action: https://s3-ap-southeast-2.amazonaws.com/awm-media/collection/E02790/screen/4166494.JPG

Something to keep in mind is that wounds from rifle fire were relatively rare. The vast majority of casualties [something like 80%] were caused by artillery. Gas was pretty high, as were 'melee' injuries inflicted within the trenches.