How can light produce electric and magnetic field when there are no accelerating charged particles? If we see light as a wave, especially in vaccum, there is nothing there, no particles, yet light has an electric and magnetic field. How can this be possible?
 A: Light is merely a manifestation of electromagnetic fields, i.e., light itself is the electromagnetic field. What we understand as light is just the propagation of electromagnetic waves, which are eventually detected by something (our eyes, a camera, etc). These waves were generated by some kind of source, such as the nuclear reactions inside a star.
A: Accelerating charged particles cause EM radiation, true. They don't cause all EM radiation. See Black-body and emission for two.
We mathematically describe light as wave-like (because that's how it behaves) but if one interprets "seeing" as the act of intercepting and interpreting light, we actually see [collections of] photons.
A theoretically perfect vacuum contains both photons which are, in fact, particles (for all their wave-like behavior in transit) and electromagnetic fields.
A: As pointed out in a comment by @PhysicsDave, there is the supposition of the existence of a field acting as a mediator of electric interaction and magnetic interaction.
The fields extends over spatial distance. That is how the interaction is envisioned. The interaction being mediated does not require particles in the inbetween space. The field extends over spatial distance.
Maxwell envisioned the electromagnetic interaction as medidated by an entity that in the absence of a source of electrostatic force or magnetic force is in a uniform state.
A source of electrostatic force is then envisioned as inducing a stressed state of that entity. That stressed state is then thought of as the mediator of the interaction.
When the source changes the stressed state changes. The electromagnetic field has the property that the rate of change of the stressed state tends to persist.
Propagation of transversal waves:
-You need some form of elasticity. If the entity is pushed into a stressed state the entity tends to return to the uniform state
-Rate of change should persist. With persistence of rate of change: when the entity is changing in the diraction towards uniform state, at some rate, then it will overshoot the zero point, and will go on towards a stressed state in the opposite direction.
Those two properties, elasticity and persistence of rate-of-change, give the electromagnetic field the ability of wave propagation. There is no necessity for particles to be present in the space; the electromagnetic field itself supports waves propagation.
A: Something, such as accelerating charge particles, caused the light to propagate. The particles don't have to accompany the light. Consider an analogy - something creates a sound wave that you hear some distance away. You could ask how could sound produce compression and rarefaction of air when there is nothing pushing on it where you are?
A: 
there is nothing there, no particles,

There is no particle there, but there is field. A charge at the rest has an associated electric field everywhere around in the space, getting smaller with the inverse of the distance squared. If we think of all existing charges, the space is full of fields.
If one of the charges is moved to another position this field changes. The EM wave is the pattern of field change, that propagates through the space with the light speed.
