When the Pilgrims set sail for America, they would have attempted to duplicate as closely as possible the foods with which they were familiar. However, they were somewhat limited due to the necessity of selecting foods that would keep on a long ocean journey. Another consideration was available room for carrying supplies. The Mayflower was described as an 180 tun ship. However, tun did not mean 2,000 pounds in the seventeenth century. A tun was a large barrel of wine (about 265 gallons). The Mayflower could carry 180 of these fully loaded tuns in the hold.
We know that the Pilgrims ate mostly cold food on the voyage consisting of salted meat and fish, beans, peas, oatmeal and other grains, hard biscuits and hard cheese and drank beer (their water was soon contaminated). An occasional hot dish may have been cooked over an open charcoal fire in a box of sand. However, for an idea of what food was taken to America on board the Mayflower, we have several sources that provide us with information. The Emigrant Ship Provisions List 1630, which is found in the Pilgrim Hall Museum (http://www.pilgrimhall.org/onmayfl.htm), gives us an idea of some of the foods that were likely taken on the Mayflower. It lists the following foods (spelling is original): 8 bushels of meale, 2 bushels of pease, 2 bushels of otemeale, 1 gallon of oyle, 1 gallon of aqua vitae, 2 gallons of vinegar and 1 firkin of butter. It also lists the following spices: sugar, pepper, clove, cinnamon, mace, nutmegs and fruit.
Another source that gives us a clue as to foods that were likely taken aboard the Mayflower is the list that Captain John Smith gives in A Sea Grammar, 1627. These include: fine wheat flour, rice, currants, sugar, prunes, cinnamon, ginger, pepper, cloves, green ginger, oil, butter, Holland cheese, wine vinegar, canarie sack, aqua vitae, fine wines, pure water, lemon juice, white biscuit, oatmeal, bacon, dried neat's tongues, beef packed in vinegar, legs of mutton (minced and stewed, close-packed in earthen pots).
One thing for certain, whatever foods were carried on the Mayflower were insufficient for a long-term diet. Fruits (natural, dried and preserved) were certainly in small supply in that day which led eventually to the development of scurvy. When the Pilgrims arrived, it was winter, and they did not have readily available foods in the New World to supplement those brought on the ship, and they were forced to exist for months primarily on the food they had brought. Due to the lack of healthy food, along with other harsh conditions, half of the passengers would be dead by spring.