First off, the "simplest" way that is popularized is to use wormholes. Whether or not this is feasible, it works by connecting two points in space time, no matter how far they are apart. It is the geometry of space that is changed so that by all definitions the points would then be nearby, although they may not appear to be nearby points at a macroscopic scale. Configurations like this are not possible in euclidean geometry, but in a more general geometry like general relativity, it is completely mathematically consistent.
Another way, is to use quantum entanglement. Two seemingly distant particles can sometimes be governed by the same wave function, so that in some sense they are the same "object". Communication could be achieved through this method, except for that it is thought to be impossible to know which particle is a member of the entangled pair. For example if a source on earth were to stream a split beam of entangled particles to mars and venus, so that a colony on mars and a colony on venus could both intercept the beam, venus and mars would be able to communicate with each other by performing specific methods on each particle. However, they would also need to determine that they were both working on the same particle, so a "coincidence counter" would need to be employed. The coincidence counter would use classical signals (like radio communications) to synchronize and determine that each was performing on the same particle. So it's ultimately STILL limited to the speed of light because of the coincidence counter.... The really cool thing though is that the information does transmit instantaneously. Mars could send a message to distant Venus instantaneously which could then be recorded on a computer hard drive. The information could be opened as a bitmap image, for example, but would be COMPLETELY random (noise). No pattern or message of any kind would be discernible. But somehow in that randomness the information is there. Once the coincidence counter's radio signal traverses the distance and arrives hours later, the information could be incorporated into the random noise and the message will appear! Neither the quantum information nor the coincidence counter's information would be sufficient by themselves. Only when the two are recombined mathematically is it possible to read the information. MAGIC! This truly is a very strange phenomenon.
There is a deep connection between information, entropy, and quantum entanglement... there might be a way.