Feast days are days that are special to a specific deity or deities. If you are looking to work with a specific deity or ask favors these are the best days to do them. Most deities have multiple feast days so if you miss one don't worry, there will be another.
Nemesis, was the Greek goddess of fortune and retribution. In Rome she is known as the balancer of life.
Vertumnus is the Roman god of the changing seasons, plant growth, gardens, and fruit trees. (Vertumnal Equinox anyone?)
The Nymphs as the personification of nature. There are many different kinds of Nymphs but most often found in forest groves and springs.
Vulcan Roman good of fire and smithing. Today is his feast day, Vulcanalia.
In honor of Vulcanalia light a fire! It can be as big or as small as you are able. Historically, offerings of small animals were given to Vulcan as a way of keeping fires out of the cities but this is the 21st century. Instead offer some of your harvest, a cutting from a houseplant or a plant from your garden or be creative! Offer Vulcan a sketch, a song, or a poem. Something that can be put on paper and burned.
Learn more about Nemesis: http://www.theoi.com/Daimon/Nemesis.html
Learn more about Vertumnus: http://www.maicar.com/GML/Vertumnus.html
Learn more about the Nymphs: http://www.maicar.com/GML/NYMPHS.html
Learn more about Vulcan: http://www.napoliunplugged.com/vulcanalia.html