It depends on the object and the location the object is coming from. In the United States, straw, hay, cotton, hemp and sawdust were common. In India, you might find objects packed in jute fiber, the raw material of burlap. That country produced almost the world's entire supply of jute until after WWII, which meant (according to Siney's The Allied Blockade of Germany, 1914-1916 p. 165) that it didn't show up in Germany once the war began.

In other parts of Asia, particularly the Philippines, you could see Manila fiber or palm leaves and fiber. Peat moss shows up just about everywhere in Europe and the United States. Eelgrass was used in the Low Countries and northern Germany ─ even the Titanic had a shipment of it on board.

This packing material was a particular concern for port agents, who feared its ability to spread disease and parasites. The Nov. 19, 1914 issue of Shoe and Leather Reporter contained strict instructions about how hay, straw and other material used for packing was to be disinfected with formaldehyde gas or some other chemical to curtail the spread of hoof and mouth disease.

In the Midwest United States, you might find corn husks or old newspapers used as packing material for things being mailed or shipped by private (non-industrial) concerns. I've run across old boxes packed in that kind of way.

If I had to pick the most common packing material in 1914, I'd go with either straw or sawdust. Sawdust is a really good insulator, which meant it was used in the ice industry all the time. It's also good for things that have a tendency to move around. You fill a box with sawdust, that object isn't going to move around at all in shipment. Straw is much cheaper than sawdust, and it's pretty much ubiquitous in places that don't have big timber operations.