Is physical contact necessary for entanglement My question is as follows: Is it absolutely necessary for particles to come into contact before they can be entangled? Has any experiment reported of particles which were never in contact showing signs of being entangled with each other?
 A: Physical contact is tricky, and it's a matter of opinion whether two atoms can actually "touch". However, it is perfectly possible for two particles to become entangled even if they never interact directly with each other.
The specific scheme is known as entanglement swapping. In essence, you start with four systems, A and B, and C and D. You produce entanglement both between A and B and between C and D, possibly at separate spatial locations. You then bring together B and C and perform a joint measurement. Based on the outcome of this measurement, you need to perform some local operations on A and D, and at the ent the two are entangled.

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The systems can be anything you want, really, For example, A and D might be ions sitting in ion traps but B and C could be photons that they emit, and which are collected and measured at some in-between location.
For more information see

Entanglement Swapping: A New Quantum Trick,  Laura Mgrdichian, Phys.org, 11 October2007

or 

Deterministic entanglement swapping: First successful implementation of a technique for quantum computers, Phys.org, 26 October 2008.

For something similar and more recent, try

Physics team entangles photons that never coexisted in time, Bob Yirka, Phys.org, 28 May 2013.

