My question is whether or not it would be possible to create an entangled state between two photons that do not share the same initial photon source and their respective sources are separated by an arbitrary distance in space. This is a curiosity of mine and I have a very basic understanding of this phenomena at present, though I am attempting to learn more. If it is the case that this is possible, I would also appreciate an explanation of why or at least have someone point me to a resource explaining this. Thank you.
If the two photons are the only systems you are considering, the short answer is no, you cannot entangle them by performing only local operations. This is a consequence of the fact that entanglement cannot increase under Local Operations and Classical Communications (LOCC) only. See http://en.wikipedia.org/wiki/LOCC for a reference.
However, as it is pointed out in the previous answer, if the photons were allowed to interact with other systems, then the answer is yes, it is possible to entangle them. One way to do this is the following: Suppose Bob in one location is in possession of one of the photons while Alice is in possession of the other, the combined system being unentangled. Locally, Bob can prepare a maximally entangled state of his photon and an additional he has with him. He then sends the latter photon to Alice, so that now they both share an entangled pair. Note that it is an entangled pair where Alice holds a different photon than the one she had originally.
If Alice wants to "transfer" this entanglement to her original photon, she can also entangle it with an additional photon she keeps locally, and then perform a Bell measurement on the photon sent by Bob and the new one she introduced. Depending on her outcome, she performs a local operation on her original photon and in the end this will be entangled with the one Bob has in his location.
What I explained in words is referred to as entanglement swapping, an operation based on quantum teleportation. For more details you can take a look at http://en.wikipedia.org/wiki/Quantum_teleportation#Entanglement_swapping.
Of course in practice, entangling two photons is bloody difficult, but I presume you were interested on whether it could be done in principle and if so, under what conditions. Also, these operations are possible in principle regardless of what physical system is used.
The answer is yes, you can entangle two photons that do not share a common source.
The trick is that that both of the photons from separate sources must be entangled with particles from those two sources. These other particles must then "interact" in some way that constrains the properties of the two photons you want to entangle.