If you are connecting a balanced (xlr) output to an unbalanced (rca) input, be careful about using an adapter. Most commercially available xlr-to-rca adapters and adapter cables short pin 3 (the "cold" signal, which on a balanced output is an actual signal, despite its name) to pin 1 (ground). Nearly all pro equipment, and a lot of consumer equipment, can tolerate that, but on some consumer equipment (depending on the design of the output driver stage) the result may be compromised sonics, or degraded long-term reliability, or immediate damage. Check with the manufacturer first.
Using an adapter or adapter cable to connect an unbalanced (rca) output to a balanced (xlr) input is no problem, though. Although of course doing that does not provide most of the noise rejection that is provided by a balanced interface (if done right, it can provide some noise rejection -- see Figure 2.1 of the reference Shadorne linked to).
As Sid indicated, using an rca cable with rca-to-xlr adapters at both ends makes no sense, although it will function (apart from the possible effects that I mentioned of shorting pin 3 to ground). The noise rejection advantages of a balanced interface occur because noise picked up in a balanced cable is presumably picked up equally on both conductors, resulting in cancellation in the differential receiver stage of the equipment the signals are going into, which responds to the difference between the voltages on the two input lines. A balanced cable makes that possible by using two identical conductors, twisted together, within an overall shield. An unbalanced rca-type cable has only one inner conductor, with the shield serving as the other conductor, and so noise will obviously not be picked up equally between the two conductors, due to the physical asymmetry.
As has been alluded to, it is important to distinguish between "fully balanced" equipment (i.e., balanced internally as well as at the interfaces), and equipment which is only balanced at its interface connectors and the corresponding input and output buffer stages.
Fully balanced design, which is normally found on only some very high end equipment (such as Ayre, BAT, and Atmasphere, to name a few examples) provides a separate channel from input to output for both the "hot" (pin 2) signal, and the "cold" (pin 3) signal. (Hot may be pin 3, and cold may be pin 2, on some equipment not made in the USA). That provides cancellation of some forms of internally generated distortion, as well as cancellation of noise picked up in the cabling. Balanced cabling with xlr connectors should obviously be used with that type of equipment.
Designs which are not fully balanced, but have balanced (xlr) interfaces, and which may offer rca interfaces as well, may sound either better or worse when the balanced interface is used. Better if noise may be a problem in the particular setup; worse if that is outweighed by the sonic effects of the additional stage that the equipment introduces into the signal path to perform single-ended to balanced or balanced to single-ended conversion.
The reference linked to by Shadorne is excellent, and well worth taking the time to study.
Regards,
-- Al