Professor Persi Diaconis of Stanford University, a professional magician who changed career and became a mathematician and statistician, made a thorough study of shuffling. He found that, if you use the riffle shuffle (the usual way card players shuffle cards: cut off about half the pack and riffle the two packets together), it takes just 7 times! If you use the overhand shuffle (another popular method) it takes 2500 times! He also studied some 'academic' shuffles that nobody uses in practice.
Diaconis, Persi (1988). Group representations in probability and statistics. Hayward, California: Institute of Mathematics.
Bayer, Dave and Diaconi, Persi (1992) Trailing the dovetail shuffle to its lair. Annals of Probability , 2 : 294-313.