Why are different frequency bands used in different countries? Why are different frequency bands used in different countries despite ITU's effort for a common frequency band use? There's got to be a reason behind this.
For instance, U.S.-based Verizon Wireless uses the 700 MHz frequency band for its LTE service while European TeliaSonera and South Korean SKT uses 1800/2600 MHz frequency bands and 850/1800 MHz frequency band, respectively.
 A: The reason for this is mainly operational, rather than to do with the laws of physics.  Radio spectrum is a very scarce resource, and is managed independently by each country's regulatory authority.  In order to allocate spectrum to a mobile operator, the national regulatory authority has to make sure that spectrum is not being used by any other services.  The spectrum that an operator would like to use for its cellular services might already be in use in that country for other purposes - radar, military communications, RFID(as mentioned in the previous answer), so the regulator has to carefully manage the spectrum to avoid conflict.
Another factor is that the spectrum required to build a modern cellular system has to be in reasonably sized contiguous chunks in order for the system to function (e.g. a spare free 50KHz of bandwidth here and there is no use!).  This puts further constraints on the regulators for allocating the spectrum.
The result of all this is a rather inhomogenous country-dependent allocation of spectrum for mobile services. If you now ask about a particular technology, such as LTE, a further complication is that a mobile operator may already be using some of the LTE spectrum for another radio technology (such as WCDMA), and may not consider it economically justifiable to switch to LTE at this time. 
So the reasons are regulatory/technological/economic rather than physical.  As far as the laws of physics go, there is a relatively small bandwidth of spectrum which has suitable radio propagation properties for cellular communications (reasonable distances, in-building penetration), so there is enormous competition for this spectrum!
A: The RFID Journal explains this succinctly.

The industry has worked diligently to standardize three main RF bands:
  low frequency (LF), 125 to 134 kHz; high frequency (HF), 13.56 MHz;
  and ultrahigh frequency (UHF), 860 to 960 MHz. Most countries have
  assigned the 125 or 134 kHz areas of the spectrum for low-frequency
  systems, and 13.56 MHz is used around the world for high-frequency
  systems (with a few exceptions), but UHF systems have only been around
  since the mid-1990s, and countries have not agreed on a single area of
  the UHF spectrum for RFID. UHF bandwidth across the European Union
  ranges from 865 to 868 MHz, with interrogators able to transmit at
  maximum power (2 watts ERP) at the center of that bandwidth (865.6 to
  867.6 MHz). RFID UHF bandwidth in North America ranges from 902 to 928 MHz, with readers able to transmit at maximum power (1 watt ERP) for
  most of that bandwidth. Australia has allotted the 920 to 926 MHz
  range for UHF RFID technology. And European transmission channels are
  restricted to a maximum of 200 kHz in bandwidth, versus 500 kHz in
  North America. China has approved bandwidth in the 840.25 to 844.75
  MHz and 920.25 to 924.75 MHz ranges for UHF tags and interrogators
  used in that country. Until recently, Japan did not allow any UHF
  spectrum for RFID, but it is looking to open up the 960 MHz area. Many
  other devices use the UHF spectrum, so it will take years for all
  governments to agree on a single UHF band for RFID.

