Regarding antioxidants, Wu et al. measured the total antioxidant capacity of 28 foods.1 I put together a chart (click to enlarge):
ORAC: Oxygen Radical Absorbance Capacity - a measure of a food's antioxidant strength.
Nuts rank fairly high. And Wu found the water-soluble components in nuts had greater radical-fighting ability (42 times greater for pecans) than nuts' fat-soluble components. So if we're just eating the oil, we're missing out.
Here's another comparison (click to enlarge) - a table of the 50 most antioxidant-rich foods (from this analysis of 1113 food samples):2
Again, walnuts and pecans score high, higher even than blueberries (per serving).
What surprised me in this analysis was that coffee (a mere 8 ounces, brewed) scored higher than a cup of raspberries or blueberries. Coffee is a bean, and beans are notably high in antioxidants. Also, when you cook foods, as this study described, you often increase antioxidant capacity.
2 Content Of Redox-Active Compounds (i.e. Antioxidants) In Foods Consumed In The United States, American Journal of Clinical Nutrition, July 2006