epilepsy

In a mouse model of epilepsy (Maximal Electro Shock), the following cannabinoids were found to be anti-convulsive (ED50)(Devinsky et al., 2014): CBD 120 mg/kg Δ9THC 100 mg/kg 11-OH-Δ9THC 14 mg/kg 8β-OH-Δ9THC 100 mg/kg Δ9THCA 200-400 mg/kg Δ8THC 80 mg/kg CBN 230 mg/kg Δ9α/β-OH-hexahydro-CBN 100 mg/kg Apart from that the doses reported above are incredibly high, it does provide a proof of principle that many cannabinoids exert anti-convulsive effects.  

Parkinson´s

In cultured midbrain neurons, CBD, THCA and THC had anti-oxidative properties. Moreover, THCA and THC were shown to be neuroprotective (Moldzio et al., 2012).

References:

Devinsky, O., Cilio, M.R., Cross, H., Fernandez-Ruiz, J., French, J., Hill, C., Katz, R., Di Marzo, V., Jutras-Aswad, D., Notcutt, W.G., et al. (2014). Cannabidiol: pharmacology and potential therapeutic role in epilepsy and other neuropsychiatric disorders. Epilepsia 55, 791–802.

Moldzio, R., Pacher, T., Krewenka, C., Kranner, B., Novak, J., Duvigneau, J.C., and Rausch, W.-D. (2012). Effects of cannabinoids Δ(9)-tetrahydrocannabinol, Δ(9)-tetrahydrocannabinolic acid and cannabidiol in MPP+ affected murine mesencephalic cultures. Phytomedicine Int. J. Phytother. Phytopharm. 19, 819–824.