Here is the deal in a nutshell…

• They are rich source of many phyto-chemical substances that may contribute to their overall antioxidant activity, including carotenes, vitamin E, and polyphenolic antioxidant compounds. Research studies have been suggestive of that these compounds help body remove toxic oxygen free radicals and thus, protect body from diseases, cancers, as well as infections. 
• Pistachios are an excellent source of vitamin-E, especially rich in gamma-tocopherol; contain about 23g per100 g. vitamin E is a powerful lipid soluble antioxidant, essential for maintaining the integrity of cell membrane of mucus membranes and skin; offers protection from harmful oxygen free radicals.
• The nuts are packed with many important B-complex groups of vitamins such as riboflavin, niacin, thiamin, pantothenic acid, vitamin B-6, and folates.
• These nuts are storehouse of minerals like copper, manganese, potassium, calcium, iron, magnesium, zinc, and selenium. 100 g nuts provide 144% of daily-recommended levels of copper. Copper is an essential trace mineral that is required in neuro-transmission, metabolism, as well as red blood cell (RBC) synthesis.

Oh come on? You need more reasons than that? 🙂 I recommend buying them without the shell, takes too long…

(Source: http://www.nutrition-and-you.com/pistachio.html)