A canon answer would be great, but not sure how likely that would be. But what keeps lightsabers from simply going through or slicing through one another?
Once focused by the crystals, the plasma was sent through a series of field energizers and modulation circuitry within the emitter matrix that further focused it, making it into a coherent beam of energy that was projected from the emitter. The blade typically extended about a meter before being arced by the blade containment field back to a negatively charged fissure ringing the emitter, where it was channeled back to the power cell by a superconductor, completing the circuit.
Basically the blade of the lightsaber is encased in a field designed to control the flow of the plasma. Because its nature (being a barrier to the plasma flowing out), it would also act as a barrier to plasma flowing in. Thus, another lightsaber's plasma would not be able to flow through the boundary of the first. Also note, this is occurring at both sides simultaneously, thus doubling its effect. The interaction of the fields is likely the cause of the unique sound effects.
This possibly also explains the deflection of blaster bolts, and other such things.
I've never found a canon explanation, and most out-of-universe explanations throw their hands up in the air and say it's not possible - "terminating lasers"? "light beams that clash"? "whooshing sounds"? MADNESS!
However, there is at least one plausible explanation that satisfies the known features of a lightsaber which explains that they would clash because they're actually (roughly) a rigid fibre optic cable.
The prime component of a light saber blade is a filament of ultra-low-loss glass, about 3 meters long, properly doped, with a perfect mirror at one end and a slightly transparent mirror at the other. The transparent end (called the input end) is connected to an energy source in the handle, and if the filament is perfectly straight, it is easy to see that this set-up is a laser, except that you don't notice so because no power emanates from the free end (usually called the noput end) - the mirror there is perfect.
Why does it not appear when turned off if there are filaments supporting the light?
When the light saber is switched off, the lasers stop working, the light pressure disappears and all the filaments coil up again in the handle. All the energy stored in the lasers is reabsorbed in the power cell in the handle, another feat that can be performed by Jedi technology only.
Personally, I'm pretty satisfied with his explanation, mainly because it appeals to me via the Rule of Awesome and I'm yet to see a better explanation of lightsabers.