The Wikipedia figures are within the range of accuracy, but leave out a great many other deaths. For example, between two and three million Russian POW's died of deliberate starvation and neglect. Well over a million civilians were killed in German bombardment of cities (Leningrad and Stalingrad being the most egregious examples in the East, but also Rotterdam, the Blitz on England, etc. in the West). Forced labor drafts from occupied territories ran into the millions, many of whom (particularly from the Eastern Front) died of malnutrition, overwork, exposure, etc. Slave labor accounted for many of these deaths.
The best estimate I've seen (and this is admittedly an estimate - we will never know the exact number for sure) is that between 12,000,000 and 15,000,000 people were killed by the Nazis, either directly or indirectly. The Russians lost at least 15,000,000 to 20,000,000 dead, and the total might be as high as 30,000,000 - although a reasonable proportion of these deaths were caused by Stalin, through mass wartime deportations, the use of penal battalions where pre-war Siberian gulag detainees were treated as human minefield clearance devices, assault troops to absorb the initial defensive fire of the Germans before more conventional units broke through when the defenders ran out of ammunition, etc.
The accepted minimum figure for total WW2 fatalities, on all fronts and from all causes, is 55,000,000. The actual figure may be as high as 80,000,, particularly given the lack of records for the Eastern Front and the Chinese campaign, where Japan slaughtered Chinese by the millions. (Just as one example, after the Doolittle Raid on Tokyo in 1942, during their search for the US airmen who had landed in China, the Japanese forces killed approximately 250,000 Chinese as punishment.) This total figure also includes those killed prior to the war, in the Chinese campaign, and also those millions who died after the war, including German and Japanese POW's held by the Soviet Union (19 out of 20 never came home), the millions who died of starvation and displacement in the Eastern Front and China, etc. It's a pretty horrifying total . . .
An excellent overview of the human cost of the war is found in the final episode of that definitive series, The World At War. The episode is simply titled "Remember" - and if it doesn't bring tears to your eyes, you don't have any understanding of mass human suffering. They were the first to put the total as high as 55,000,, back in the 1970's, and this is now regarded as conservative, following the opening of Soviet archives after the fall of Communism, and the unsealing of government records during the 1990's.