CBG is the result of CBGA going through decarboxylation. Like CBGA, CBG is rarely found in cannabis extracts because its acidic precursor is converted to other cannabinoids by enzymes in the plant before it can be extracted and decarboxylated.

Research on CBG is more prevalent than research on its acidic precursor but still limited thanks largely to the legal restrictions surrounding cannabis and cannabis research.
CBG is the subject of a lot of interest as it has demonstrated a large number of medicinal properties including anti-nausea, analgesic (pain relieving) and anti inflammatory properties.
http://www.ncbi.nlm.nih.gov/pubmed/11152013
http://link.springer.com/article/10.1007/s00213-010-2157-4#/page-1
A 2009 study demonstrated potential for CBG to provide similar benefits to THC for glaucoma with out the psychoactive effects associated with THC.
http://online.liebertpub.com/doi/abs/10.1089/jop.1990.6.259
CBG has also demonstrated the ability to grow new brain cells and has even shown some anti cancer properties akin to that of THCA by blocking the receptor TRPM8.
"Italian researchers at the University of Naples assessed the effects of CBG on colon cancer and noted both anti proliferative and pro apoptotic effects". This research suggest potential for CBG to be used in cancer treatments for specific cancer types.
Though it lacks any clinical, or even preclinical, evidence there is significant anecdotal evidence from real life cases that CBG may be an effective treatment for epilepsy with the most notable case being a young boy called Jayden David who is currently taking a high CBG extract as a treatment for his Dravet's syndrome.
http://edition.cnn.com/2012/12/10/health/medical-marijuana-child/
CBG has also shown potential as an anti depressant and has demonstrated the ability to block CB1 receptors and prevent THC from activating that receptor, which would essentially block the psychoactive effects, though may also detriment many of the medicinal properties that utilise that receptor.