Actually, satellites' time goes faster than on Earth surface, due to weaker gravity field* at high altitude. This effect is way more prominent than the pitiful orbital velocities (compared to relativistic velocities), which can be handled very well with classical physics and don't really cause any significant** time dilatation.
Also, you need to remember that special relativity is indeed very special and in it's simplest form it is limited to constant motion (constant relative velocity); anything else and things get real complicated real soon. Satellites don't travel at constant velocity... round and round they go and go, where (and when) they stop, who knows...
*Yes, I know that gravity isn't actually a field force in general relativity, but it gets complicated if I say that at high altitude the space and time are less stretched by the mass/energy of Earth, thus making time go faster...
** Yes, there is an effect of time dilatation due to orbital velocity, but it's very very small. Gravitation potential difference makes a much more prominent change in the measurements of time on surface and orbit.
As to what time dilatation is - it is real, obviously. There is no other way that myons borne of cosmic radiation bombardment in the upper atmosphere could ever get to Earth's surface - their half-life is way too short and they should by all experimental data be decimated before reaching the surface... but, as their velocity is so great, their observed half-life lengthens, as the rate of time passage slows down for those fast particles.
Photons are interesting buggers, by the way... they do have momentum, and energy, but according to my knowledge they do not (or rather,
should not) have gravitational effect on their surroundings. After all, photon's energy always consists of relative energy - the observed energy of the photon depends solely of the relative motion between the observer and the photon, and obviously the energy of the photon in the emitter's inertial frame. And relative (aka kinetic) energy does not cause gravitational effects, since it would mean that all the fast-moving particles such as neutrinos should be collapsing to small event horizons... which doesn't happen, quite obviously.
By the way, ever thought what is the photon's energy in it's own reference frame?
EDIT: The direction of relative velocity doesn't make a fundamental difference in the time dilation itself, but it obviously does affect observations. A good example of what the directions affect (or rather, don't affect) is the "twin paradox", which obviously isn't a paradox at all after you go through it a few times carefully...
