In most cases, the answer is yes. But all agricultural (read: food) items must be declared. Travelers, confronted with warning signs placed above large trash cans, sometimes dump foods that they can bring in without any problems.
The one solid exception? Meat products are not allowed, whether canned, preserved, in sausage form, or any other form.
The official USDA list of allowable foods and plant products from most countries is subject to change. This list applies to almost every country, not just Greece.
Bamboo, dried poles only, no green at all
Beads made of seeds (but not jaquirity seeds)
Breads, cakes, cookies, and other bakery goods
Candies
Cheeses, hard, fully cured (but not cottage cheeses)
Coconuts (but husks or milk must be removed)
Coffee, roasted beans only
Dried foods, including milled rice, beans, and tea
Fish
Flower bulbs (but not crocosomia, gladiolus, and watsonia bulbs from Africa, Argentina, Brazil, France, Italy, Malta,
Mauritius, Portugal, or Uruguay)
Flowers, most fresh or dried kinds (but not with roots), except
eucalyptus
Fruits, canned or dried products only
Herbarium plants (but not witchweed)
Herbs, dried, for medicinal use
Mushrooms
Nuts (but not chestnuts or acorns or nuts with outer husks)
Sauces, canned or processed
Seaweed
Seeds (Seeds of flowers and vegetables are generally enterable.
Seeds of woody trees and shrubs require a nursery stock
permit from PPQ.
Shamrocks, without roots or soil
Soup and soup mixes (but not those containing meat)
Spices, dried (but not curry leaves)
Straw animals, hats, baskets, and other souvenirs (but not
items stuffed with straw)
Vegetables, canned or processed
--USDA
The Customs Department provides a slightly different list. It includes: Aloe Vera (above ground parts)Aloe Vera (above ground parts) Bat nut or devil pod (Trapa bicornis) Breads, cakes, cookies, and other bakery goods Candies Cannonball fruit Chinese water chestnut Coffee (roasted beans only) Fish * Flower bulbs Fruits, canned Garlic cloves (peeled) Lily bulbs (Lilium spp.) for planting Maguey leaf Matsutake Mushrooms Nuts (roasted only) Palm hearts (peeled) Sauces, canned or processed Seaweed * Seeds for planting or consumption Shamrocks leaves without roots or soil St. John's Bread Singhara nut (Trapa bispinosa) Tamarind bean pod Truffles Vegetables, canned or processed Water chestnut (Trapa natans) Aloe Vera (above ground parts) Bat nut or devil pod (Trapa bicornis) Breads, cakes, cookies, and other bakery goods Candies Cannonball fruit Chinese water chestnut Coffee (roasted beans only) Fish * Flower bulbs Fruits, canned Garlic cloves (peeled) Lily bulbs (Lilium spp.) for planting Maguey leaf Matsutake Mushrooms Nuts (roasted only) Palm hearts (peeled) Sauces, canned or processed Seaweed * Seeds for planting or consumption Shamrocks leaves without roots or soil St. John's Bread Singhara nut (Trapa bispinosa) Tamarind bean pod Truffles Vegetables, canned or processed Water chestnut (Trapa natans)
And Mythos Beer fans? Sorry, but you are only allowed one liter or 33.8 oz of alcohol, and even that may vary depending on the laws of the state you arrive in.
For the full Customs Department list of approved and unapproved products, and other information, go to the USDA website. And this is another useful page from the US Consulate in Canada: Returning to the US
Please note: approved items are subject to change. If you have a question on a particular item, contact Customs directly. The above items just apply to US citizens returning to the US from abroad. Citizens of other nations will have different restrictions and requirements.
