There are a number of games who depict planets as one general climate such as Desert or Tundra for example. I know that games only do this to save time and money and obviously, this is not evident on Earth (but if conditions were like this surely this would be only in extreme circumstances). So I want to know whether it is possible to have a planet with just one climate and if so, how what circumstances need to take place before that can happen?
I think your choices are very, very cold or very, very hot :P
Even Pluto and Mercury probably have local climate variances if you squint hard enough though. Something like Europa is probably pretty homogenous under the ice, at least from our perspective (though I imagine the Europans prefer to live near the warm core away from the solid ice poles and the cracking surface ice :). The moon is geologically/tidally active so maintaining liquid water isn't dependent on external heat source.
Anything within the "goldilocks zone" of a star will have poles and an equator unless it has a very bizarre orbit or virtually no land features that could interrupt constant water or air flow to distribute heat evenly across the planet.