Is an approval required to fly from the right seat?
As Ron mentions in the comments here in the US it is not illegal by any specific regulations however... 

Most GA aircraft (the smaller ones at least) only have a single set of instruments that reside in front of the left seat as you mention in the question. Lets say hypothetically you were flying right seat and something went wrong. Due to the angle of view you were not able to read an instrument and this lead to an accident. Lets say you lose your primary CDI/Glide Slope while flying an ILS approach and you need to use one on the far side of the cockpit. For some reason you are alone and in the right seat. If an accident did occur as a result of this you may be able to be held to 


  §91.13   Careless or reckless operation. 
  
  (a) Aircraft operations for
  the purpose of air navigation. No person may operate an aircraft in a
  careless or reckless manner so as to endanger the life or property of
  another.


Since the left seat was open and available for you. But other than that there is no regulation preventing such operation. 

Ron  posted an excellent article in the comments below that has at least one quote worth mentioning 


  Aircraft insurance policies and flying club rules often specify that
  all flying is to be done from the left seat unless the pilot holds a
  current flight instructor certificate or has specific authorization.


While this is not an FAA regulation insurance companies or the rental/flight club you get your plane from may stipulate left seat only flying.