What are the best exercises to increase flexibility?
yoga! 6,000 yrs old and still effective/practical for the modern age.
Try a beginner yoga dvd or class in your area. You can learn some yoga and do 10-20 or more routines on your own at home, in general or before or after other workouts.
I recommend beginner yoga dvd’s on this:
http://www.sunlightyoga.com/stacies-picks-yoga-dvds-cds–books.html