Evidence from Greenland ice cores shows that year-to-year temperature variability was probably higher in some past cold periods, but there is considerable interest in determining whether global warming is increasing climate variability at present. This interest is motivated by an understanding that increased variability and resulting extreme weather conditions may be more difficult for society to adapt to than altered mean conditions. So far, however, in spite of suggestions of increased variability, there is considerable uncertainty as to whether it is occurring. Here we show that although fluctuations in annual temperature have indeed shown substantial geographical variation over the past few decades, the time-evolving standard deviation of globally averaged temperature anomalies has been stable. A feature of the changes has been a tendency for many regions of low variability to experience increases, which might contribute to the perception of increased climate volatility. The normalization of temperature anomalies creates the impression of larger relative overall increases, but our use of absolute values, which we argue is a more appropriate approach, reveals little change. Regionally, greater year-to-year changes recently occurred in much of North America and Europe. Many climate models predict that total variability will ultimately decrease under high greenhouse gas concentrations, possibly associated with reductions in sea-ice cover. Our findings contradict the view that a warming world will automatically be one of more overall climatic variation.