In 2008 the researcher Alexei Koudinov (Doping Journal, 2008, 5: 2-10) observed that Michael Phelps kept listening to music on the headphones up to a few seconds before entering the pool at the Olympics in Beijing, where he won 8 gold medals. 

In his article Koudinov eventually accused Phelps of doping in accordance with the WADA Code, which prohibits "any artificial increase in the transport and transfer of oxygen". 
Indeed, many scientific studies show that listening to music can modify the efficiency of breathing and increase Hb saturation, effectively improving the transport of oxygen to the muscles. 

Listening to music before or during the effort has a relaxing effect on the musculature, reducing the consumption of O2 for those muscles not engaged in the action, therefore increasing the oxygenation of the muscles involved in the gesture. Even coordination and brain-muscles communication gets better, economizing energy expenditure, with a "mechanism of bio-chemical feedback derived from an external source": music, precisely. 

A recent study (Pre-task Improves swimming music performances, J Sports Med Phys Fitness, 2014) demonstrated that listening to music 5min (self selected) up to 1min before the race (200m free-style) improves the performance time by about 2" (1.44%) in a group of swimmers of regional level, compared to the control group, which was to race in silent conditions. 
Another 2014 study (Music Enhances performance and perceived enjoyment of sprint interval exercise, Med Sci Sports Exerc) detected an improvement in peak power and average power in 4 repetitions of 30sec "all-out" efforts on a cycle-ergometer, separated by 4 min recovery, in a group of moderately trained young adults. 
Already in 1998 (Int J Sports Med, 19: 32-37) it was noticed that listening to music for 15min running at 70% of VO2max showed significant reductions in heart rate (from 152.9 to 145.9 beats/min), systolic blood pressure (from 158.1 to 151.7 mmHg) and lactic acid (from 2.75 to 2.13 mM/l in well trained men. 

Another study on elite triathletes (J Sci Med Sport, 2012; 15: 52-57) engaged in running, shows an extension of the "time-to-exhaustion" by 19% when listening to music. Lactate also resulted lower and O2 consumption was reduced by 1% at the same speed. The gesture of running is more economical as well. 
The authors conclude that "Music produces ergogenic benefits, psychological and physiological". 

Personally, trying out myself while engaged on some cycle-ergometer training, and listening to songs from The Doors, always the same ones, I noticed a reduction in the feeling of fatigue as well as decreased lactate concentrations at a given heart rate. Probably those musical rhythms I am so keen on, induce those neuromuscular feedback mechanisms, sensibly improving my performance.