The tradition of the Pilgrims' first Thanksgiving is steeped in myth and legend.  Few people realize that the Pilgrims did not celebrate Thanksgiving the next year, or any year thereafter, though some of their descendants later made a "Forefather's Day" that usually occurred on December 21 or 22.  Several Presidents, including George Washington, made one-time Thanksgiving holidays.  In 1827, Mrs. Sarah Josepha Hale began lobbying several Presidents for the instatement of Thanksgiving as a national holiday, but her lobbying was unsuccessful until 1863 when Abraham Lincoln finally made it a national holiday with his 1863 Thanksgiving Proclamation.

Today, our Thanksgiving is the fourth Thursday of November.  This was set by President Franklin D. Roosevelt in 1939 (approved by Congress in 1941), who changed it from Abraham Lincoln's designation as the last Thursday in November (which could occasionally end up being the fifth Thursday and hence too close to Christmas for businesses).  But the Pilgrims' first Thanksgiving began at some unknown date between September 21 and November 9, most likely in very early October.  The date of Thanksgiving was probably set by Lincoln to somewhat correlate with the anchoring of the Mayflower at Cape Cod, which occurred on November 21, 1620 (by our modern Gregorian calendar--it was November 11 to the Pilgrims who used the Julian calendar).  

There are only two contemporary accounts of the 1621 Thanksgiving:  First is Edward Winslow's account, which he wrote in a letter dated December 12, 1621.  The complete letter was first published in 1622, and is chapter 6 of Mourt's Relation: A Journal of the Pilgrims at Plymouth.

The second description was written about twenty years after the fact by William Bradford in his History Of Plymouth Plantation.  Bradford's History was rediscovered in 1854 after having been taken by British looters during the Revolutionary War.  Its discovery prompted a greater American interest in the history of the Pilgrims, which eventually led to Lincoln's decision to make Thanksgiving a holiday.  It is also in this account that the Thanksgiving turkey tradition is founded.

The following is a fairly complete list of the foods available to the Pilgrims during the three-day Thanksgiving harvest celebration. As can be seen in the above two quotations, the only foods specifically mentioned by the Pilgrims are: "corn" (wheat, by the Pilgrims usage of the word), Indian corn, barley, peas (if any where spared), "fowl" (Bradford says "waterfowl"), five deer, fish (namely bass and cod), and wild turkey.  

FISH:  cod, bass, herring, shad, bluefish, and lots of eel.

SEAFOOD:  clams, lobsters, mussels, and very small quantities of oysters

BIRDS:  wild turkey, goose, duck, crane, swan, partridge, and other miscellaneous waterfowl; they were also known to have occasionally eaten eagles (which "tasted like mutton" according to Winslow in 1623.)

OTHER MEAT:  venison (deer), possibly some salt pork or chicken.

GRAIN:  wheat flour, Indian corn and corn meal; barley (mainly for beer-making).

FRUITS:  raspberries, strawberries, grapes, plums, cherries, blueberries, gooseberries (these would have been dried, as none would have been in season).

VEGETABLES:  small quantity of peas, squashes (including pumpkins), beans

NUTS:  walnuts, chestnuts, acorns, hickory nuts, ground nuts

HERBS and SEASONINGS: onions, leeks, strawberry leaves, currants, sorrel, yarrow, carvel, brooklime, liverwort, watercress, and flax; from England they brought seeds and probably planted radishes, lettuce, carrots, onions, and cabbage.  Olive oil in small quantities may have been brought over, though the Pilgrims had to sell most of their oil and butter before sailing, in order to stay on budget.

OTHER:  maple syrup, honey; small quantities of butter, Holland cheese; and eggs.

Ham.  (The Pilgrims most likely did not have pigs with them).

Sweet Potatoes-Potatoes-Yams.  (These had not yet been introduced to New England).

Corn on the cob. (Indian corn was only good for making cornmeal, not eating on the cob).

Popcorn.  (Contrary to popular folklore, popcorn was not introduced at the 1621 Thanksgiving.  Indian corn could only be half-popped, and this wouldn't have tasted very good.)

Cranberry sauce.  (Cranberries were available, but sugar was not.)

Pumpkin Pie:  (They probably made a pumpkin pudding of sorts, sweetened by honey or syrup, which would be like the filling of a pumpkin pie, but there would be no crust or whipped topping.)