Balanced connections are commonly used for live audio and in recording studios for microphones with long cables. Long cables (30 feet or more) carrying microphone (low voltage, 1-3 mV) or guitar pick-up signals can pick up noise from EMI or RFI. Balanced connections along with the differential circuits required inside the electronic gear can cancel out this noise. Read about it here:
http://en.wikipedia.org/wiki/Balanced_audio
In pro audio, balanced interconnect cables, with XLR plugs, have become standard for all situations. Having both balanced and unbalanced cables would just create unnecessary expense and confusion. In home audio, RCA plugs on unbalanced connections have long been the norm. RCA plugs are smaller, taking less space on crowded rear panels of electronic gear. In most homes, much shorter interconnect cables are used, and there is typically much less EMI or RFI noise. In home audio, the only signal sources with very low voltages (similar to microphones) are phonograph pick-ups. They are single-ended sources, unbalanced, and use shielded cables with RCA plugs. In most cases, they do not suffer from EMI/RFI noise.
It seems that balanced connections have become fashionable for preamp-to-amp connections. Many products offer these as a highly sought-after feature, usually at higher prices. The voltage levels between preamps and amps are much higher than microphone level, roughly 100 times higher. Interconnects at this level are much less prone to induced EMI or RFI noise, especially if they are less than 30 feet long. Standard RCA interconnects between a preamp and amp are fine, unless you have an unusually noisy environment with high levels of EMI or RFI. Its not worth paying a premium price just to have an amp with pro-style balanced inputs.