Converting chemical energy into motion can be done on a molecular level with synthetic molecular motors and on a larger scale regular molecular motors facilitate the motion of proteins and cells. In the macroscopic world the mercury beating heart and the tears of wine demonstrate how certain chemical phenomena can also drive motion.
The so-called camphor boat (Nakata et al. 2006 DOI) is an example of current research into autonomous motion. It consists of a small disk (3 mm diameter) of camphor or camphanic acid mixed with KBr (think IR spectroscopy) which is placed on water in a petry dish. It cannot be avoided that the disk is slightly asymmetric and as the acid slowly dissolves in water, a camphanic acid layer that forms around the disk is also asymmetric. The disk will then move in the direction of the water with lower concentration of camphanic acid due to the higher surface tension (see the Marangoni effect for the physics involved) and hey presto, autonomous motion!. Added surfactants can make the motion stop and resume again reminiscent of a chemical clock.
Another self-propelled system, demonstrated by the Whitesides group, consists of placing a small disk of platinum in a hydrogen peroxide solution filled tub. As the metal is oxidized by the peroxide, bubbles of hydrogen gas escape from its underside providing the propulsion (Ismagilov et al. 2002 DOI). The Pt disk is coated with PDMS with one side made hydrophilic by plasma oxidation and this enables two disks to attract each other creating a form of self-assembly. Multiple chiral disks (adjusting PDMS shape and position platinum "eye") can mimic swarming behaviour of animals.
What is still missing in these exploits is of course directed motion. In a peculiar segmented platinum/nickel/gold/nickel/gold nanorod (length 1.5 micrometer) / hydrogen peroxide system, the Pt segment as before provides the locomotion (explanation is slightly different: dissolved oxygen causing a surface tension gradient) and an applied magnetic field align the rods through the nickel segments (Kline et al. 2005 DOI). The scientists responsible were able to coerce the nanorods into spelling their university's call sign and there are worse ways to spend your Sunday afternoon.
A most recent contribution from the Jean Fréchet group goes to show that you can even use light to directly and controllable propel objects floating on a liquid. Well known manifestations of converting light to work are the Crookes radiometer and the solar sail. The novelty approach (Okawa et al. 2009 DOI) consists of a small block of PDMS (millimeter scale) covered on one side with a so-called carbon nanotube forest material. This is the blackest known material and any incident light is effectively converted to heat which in turn heats up the liquid surface which in turn creates a surface tension gradient and ultimately motion. With a modest speed of 8 cm/s this device still outperforms the other contestants but the race is far from over.