Technically, they aren't affected by gravitational fields because of mass. Rather they are affected by gravitational fields because of the changes to the space-time dimension caused by the gravitational field. They react to the space-time disruption, not to the gravitational field itself. For more information on this, see NASA's website at http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961102.html

Photons AT REST have no mass but no photons are never at rest and therefore have energy thus some mass. Thats why when you get to the point of energy in gamma rays and cosmic rays the line between wave/particle and particle starts to blur. So in essence photons have a small ammount of mass and are therefore able to be affected by gravity.

To clarify: according to relativity, E= MC^2. Photons have an energy, E, ergo they have a mass M = E/C^2. Also, according to the theory of relativity, gravitational fields actually curve the space-time around them: photons always go in a straight line, but on a curved surface, this means that they will appear to bend in certain frames of reference.

According to Newton's theory of gravitation, photons of light would be unaffected by gravity, as you say, because they have no mass. (Not, of course, that Newton knew that light travelled as photons, or even that it was an electromagnetic radiation.) However, according to Einstein's general theory of relativity, gravitation works not simply by creating an attractive force between masses, but by curving space aroung a massive object. Observation of whether and how starlight was bent during a total eclipse in 1919 was the first practical test of the general theory. The observation vindicated the theory. Newton's gravity model would not have bent the light. If you want to picture how it works, think of a large round freestanding swimming pool which is covered by a taught rubber cover. The rubber sheet represents in 2 dimensions our three dimensional space. Now get some heavy iron balls to represent the sun or the planets or other massive objects and throw them on the cover. They will produce dips in the rubber. Project a stream of light marbles across the cover at high speed to represent the photons. The marbles are so light that they will not create an indent in the rubber so they represent massless photons. However they will still be deflected by the dips or gravity wells. Furthermore you'll see that any heavy balls that are fairly close to each other will be attracted. This is of course a rather simplified picture but it gives you the idea. Please don't jump to any conclusions about the nature of the 3rd dimension we have added for the dips. Its only a model!