Wiki sums up the complete protein question pretty well:
Generally, proteins derived from animal foods (meats, fish, poultry, cheese, eggs, yogurt, and milk) are complete, though gelatin is an exception. Proteins derived from plant foods (legumes, grains, and vegetables) tend to have less of one or more essential amino acid. Some are notably low, such as corn protein, which is low in lysine and tryptophan.
Certain traditional dishes, such as Mexican corn and beans, Japanese soybeans and rice, and Cajun red beans and rice, combine grains with legumes to provide a meal that is high in all essential amino acids.
Most unrefined foods contain all the essential amino acids on their own in a sufficient amount to qualify as a "complete protein". Foods that also obtain the highest possible Protein Digestibility Corrected Amino Acid Score (PDCAAS) score of 1.0 are certain dairy products (including whey), egg whites, and soy protein isolate. Other foods, such as amaranth, buckwheat, hempseed, meat, poultry, Salvia hispanica, soybeans, quinoa, seafood, and spirulina also are complete protein foods, but may not obtain a PDCAAS score of 1.0. However, most unrefined plant foods (excepting fruits) provide more than enough of all essential amino acids even after you account for any differences in digestion or protein quality.