We've been using EMF to transmit energy (information) for over a century. I was wondering is there any other way to send a message on long distances, even faster than EMF waves can travel? For example there are particles that travel faster than C. Or as another example I have heard the Quantum Entanglement can be useful in this case.
Electromagnetic waves travel at the speed of light, and nothing can carry energy or information faster than light. Quantum entanglement doesn't carry information from one particle to another: all you get on one end is a random value from some distribution that has a relationship to a random number somewhere else. They can't be used to transmit information back and forth between each other.
There are some general relativistic effects that allow space itself to travel faster than light, but getting this to work in any sort of practical sense requires negative energy density and other weird stuff that may not be possible. Check out this for more information.
There are of course lots of ways to transmit information slower than light without using electromagnetic waves. The most common is to use matter: write something down on paper, then move the paper to the intended recipient of the message.
In principle, any of the fundamental "forces" could be used to transmit information. In practice, humans are only able to use electromagnetism. And in any case, none of these "forces" travel faster than light. Gravitational waves basically travel as fast, but no faster. Any massive particles (including neutrinos) will travel strictly slower than light. And entanglement does not actually allow transmission of signals faster than light.
It is, of course, possible to communicate by sending massive particles from one place to another. But this is not useful because they could only really travel through vacuum and would be susceptible to interference. And in any case, we would need some force to accelerate them for the transmission, so we can boil the choice down to the four fundamental forces. Below, I'll explain why electromagnetism is useful, and others are less so.
Electromagnetic waves are easy for us to manipulate for several reasons. First, there is the fact that the type of matter that forms at energies and densities we experience is primarily atomic or molecular -- rather than a quark soup or glueballs, for example. And photons are massless, which means you don't need to give them extra energy just to exist, which means it's pretty easy to create them. Also, human-scale energy levels are sufficient to strip electrons from those atoms, or just move them around. This leads to the emission and absorption of photons, which we use to transmit information. The reverse is also true; passing electromagnetic waves affect matter pretty strongly. This is why we can use electromagnetic waves so effectively for transmitting information.
The weak nuclear force (*) is much harder to interact with. The reason for this has a lot to do with the masses of its force carriers, the W and Z bosons -- nearly 100 GeV. This means that you do need to give them a lot of extra energy just to exist. So any interaction involving them will need to be very energetic, and is likely to release a lot of energy (of order 100 GeV, usually). It's hard to direct all that energy into appropriate reactions without accidentally sending some into the wrong place, so you end up destroying molecules, and generally ruining someone's day. And even then, the only signal that could travel very far might be neutrinos, which are notoriously hard to detect -- mostly because they don't interact electromagnetically. In principle, it's possible. But it's just not practical for humans to produce these signals safely or detect them efficiently. The strong nuclear force will require even more energy, so you'll have lots of energy moving around destroying things, and there's nothing you would call a signal that would come out.
The final candidate among the fundamental "forces" is gravity. And there certainly is a way for information to travel in the form of gravitational waves. Hopefully, lots of interesting astrophysical systems are using gravitational waves to tell us what they're up to. But it is taking enormous effort just to try to detect the gravitational waves produced by black holes, neutron stars, and white dwarfs colliding with each other, so detection is clearly not efficient. And production takes enormous masses moving at enormous speeds, so that's not exactly cost effective. We use too much energy just driving cars around, never mind accelerating enormous objects to extraordinary velocities just to say hello.
Since the Standard Model just has the four forces discussed above, we're only left with electromagnetism. You'll have to come up with a new theory for any alternatives. And there's nothing we take very seriously that could possibly go faster than light. This includes quantum entanglement, as far as we currently know.
So, to summarize: yes, it's possible in principle, but no, it's not practical for humans to do so.
(*) Note that electromagnetism and the weak force are unified at high energies into the "electroweak force". But at typical human energy scales, these split nicely into the weak and electromagnetic forces.
I am highly skeptical about faster-than-light transmission, but it is possible, at least, in principle, to transmit information with antineutrinos by controlling power of nuclear reactors (see, e.g., http://arxiv.org/abs/0704.0891 or http://www.phys.hawaii.edu/~jgl/post/gigaton_array.pdf ).
EDIT(07/05/2013): I have found out that an experiment on information transmission with neutrinos was actually conducted recently, using the Fermilab NuMI neutrino beam and the Minerva detector. Distance - about 1 km, including over 200m of rock, data rate - 0.1Hz, error rate - 1% (published in Modern Physics Letters A, http://www.worldscientific.com/doi/pdf/10.1142/S0217732312500770 or http://arxiv.org/abs/1203.2847 ).