The 12 spacecraft sent to or sent past Mars have taken between 128 to 333 days from Earth, as of January 2015. Travel between Earth and Mars varies significantly and depends largely on the positions of the planets in relation to each other as well as the spacecraft propulsion system.
NASA's New Horizons probe is the fastest spacecraft launched from Earth as of January 2015. It traveled at 36,000 miles per hour when it was launched in 2006. If it had traveled to Mars during the closest approach to Earth, it could have arrived in as little as 39 days.
Generally, after a Mars-bound craft is launched, it detaches from the weighty launch vehicle and achieves maximum velocity soon after. A rocket motor and attitude jets provide course correction for the craft as it travels.