Anthocyanins are the largest group of pigments in the plant kingdom. They are molecules, usually found in plants, which are responsible for the red to blue color spectrum in nature. There are more than 635 known anthocyanins.
Preliminary evidence suggests that some anthocyanins have anti-oxidant and anti-inflammatory properties, but further research is needed to determine if these effects are practical in terms of oral supplementation.
Plants tend to contain a wide range of anthocyanins. These compounds are also responsible for the leaves changing color in autumn.
Blue pigmentation, Purple pigmentation, Deep red Pigmentation
Anthocyanins are a very fun area to study. They seem to provide a lot of benefit, but there are so many factors affecting whether they get into your body or not (and how they work afterwards) that supplementing anthocyanins effectively and economically seems like a Pipe Dream.
For now, eat your blue-red plants.
Most scientific support for anthocyanins can be found on the respective molecule's own page.
(Common misspellings for Anthocyanins include anthocyanin, anthocianin, anthosianin, anthosyanin, anthosyanins)