Even a solitary person can enjoy a communal feast with the Gods. Ancient, unbreakable oaths ensure this. Traditionally, the feast is accompanied with activities appropriate to the occasion. For instance, if you feast to celebrate the patron deities of crafts, it is traditional to celebrate with some crafts.
The particular occasions for feasting with the Gods varied from person to person and polis to polis in ancient times, and they continue to vary today. Here is a list of some occasions you may wish to observe with a sacred communal feast, whether alone or with a group. Examples from ancient festival calendars are provided, so you can easily research how the ancients feasted. But we do not gather to celebrate the ancients! It is possible to reconstruct the ancient ways without dogmatic reproduction of details incompatible with modern life.
Examples: Panathenaia, Kallunteria, and Plunteria
Concept: This is a time to replace tattered shrine decor, cleaning dusty statuary, and generally attend to the periodic needs of the physical worship space.
Examples: Genesia and Diasia
Concept: This is a solemn (but not necessarily depressing or negative) occasion on which to remember those who have died. One may also offer thanks and petitions to a deity associated with compassionate dealings with the dead (such as Zeus Melikhios).
Example: Puanepsia
Concept: This should be tailored to be meaningful to you or your community. If you are a tax accountant, the time of year and type of "harvest" you come to look forward to will be different from that of a wheat farmer. Honoring a deity associated with your kind of harvest and trade is more ideal than honoring the deity appropriate for a certain group thousands of years ago in a different climate and culture.
Example: Khalkeia
Concept: In the festival of Khalkeia, Athena and Hephaistos (although many people mistakenly only associate him with blacksmithing) were celebrated as patrons of craft, innovation, art, and creative expression.
Example: Apatouria
Concept: Get together to feast with family members (whether or not they share your religious preferences) and honor the deities who have been kind to your family and to family in general. Basically a family reunion, this is a chance to note births, deaths, marriages, and other changes in the family cycle. With a little creativity, it is often possible to offer a public libation to such deities (and spirits, if applicable) without offending the sensibilities of others. Even in a family dominated by members of one of the monotheistic religions, offering thanks to God (Zeus Phratria) is an honorable mix between traditional practice and respect for the family.
Example: Thargelia
Concept: In various ways (psychological and physical being fairly obvious), we stand to benefit from a periodic leaving behind of the unhealthy and fresh embrace of the healthy. This can be a period of laying off of junk food and reduction of caffeine leading up to a healthy (but exceptional) feast. One may also celebrate by taking a few days to intentionally avoid offending others, playing head games with people, and generally acting terrible. Always end with a celebration and thanks for divine aid and refreshment.