Tamasic foods are those that have a sedative effect on the mind and body. In general, they are considered detrimental. According to yoga, these foods are to be avoided as they can cause mental dullness and physical numbness. However, in times of pain they are allowed to alleviate suffering.
Examples include: meat of an animal, fish, the fertilized egg, onion, garlic, scallion, leek, chive, mushroom, alcoholic beverages, durian, blue cheese, eggplant, opium, and any food which has been kept overnight before consumption.
Rajasic foods are those that have a stimulating effect on the mind and body. They are considered to be neither beneficial nor harmful. These foods lead to aggressiveness and irritability, and are often obtained in a way that harms another organism.
Examples include: caffeinated drinks (such as coffee, tea (both black and green), cola drinks, and energy drinks), brown or black chocolate, paan, ginkgo biloba, overly spicy food, salty food, and the unfertilized egg.
Sattvic foods are those that lead to clarity of mind and physical health. These foods are to be consumed on a regular basis. Sattvic foods are generally those which can be obtained without harming either another organism or one's self. Only Sattvic foods are acceptable as offerings to the Hindu gods, with rare exceptions.
Examples include: water, cereal grains, legumes, vegetables, fruits, nuts, unpasteurized and unhomogenized fresh milk and all fresh milk derivatives (mostly ghee, but also butter, cream, fresh or cottage cheese (paneer), and yogurt (lassi)), and raw honey.
Eggs are a very complicated case and don't have a clear cut answer. Since there's debate as to the validity of the sources that categorize it as Tamasic or Rajasic, I'd like to provide some moral insight here.
Specifically, I want to address "vegetarian eggs". A "vegetarian egg" or an egg without an embryo developing in it is produced when a hen does not mate with a rooster before laying the egg.
I have been taught that one reason such eggs are not considered suitable for consumption is that by preventing fertilization you are preventing the birth of an animal, which is considered unjust by some. The reasoning here is that blockading the creation of life is similar if not equal to extinguishing it.
Again, I don't have a source for this besides the personal teachings of my parents and gurus, so if someone has a reference from the scriptures that would be very helpful!
Sources (please add more as you edit, and remember to paraphrase):