Yes, genetic modification works, and works well. The techniques have been applied successfully for human medicine, agriculture and industrial applications.
a) all the human insulin needed by diabetics is made by genetic modification in bacteria. It is perfectly safe and has been completely accepted by all;
b) chymosin, a substitute for rennet from the intestinal lining of calves is made by genetic modification in bacteria and is used to make "vegetarian" cheese;
c) large amounts of GM crops have been grown in North and South America including cotton, maize and soybean. In the case of soybean, more than 50% of the global soybean crop is GM.
M. Koornneer (2002). M. Classical mutagenesis in higher plants, in Molecular Plant Biology, 1, chapter 1. Oxford University Press (http://www.oup.co.uk/pdf/0-19-963875-6.pdf)
B.S. Ahloowalia (1998). Topical Report: Multiplying the Benefits Radiation Techniques in Plant and Crop Breeding. IAEA Bulletin, 40, 37-39 (http://www.iaea.or.at/worldatom/Periodicals/Bulletin/Bull403/article7.pdf)