Some models are - but there are a few specs you should be looking out for. A long battery life, the ability to hear your surroundings, and on-ear controls are three key factors in choosing a good pair of running headphones.
You should also look for earbuds with IPX4 water resistance ratings or above, as they'll be protected from a little sweat or rain if you jog outside.
Of course comfort and fit are hugely important too - so look for Sony earbuds with interchangeable eartips in a range of sizes.