The number of executions under Stalin varies between 642 980 (source: Zuyev M.N. 2002. History of Russia Vol. 2: p.230) (the internal report on the number of convicted to death penalty to Khrushchev for 1921-1954) and 827 995 (source: Pozdnov M. Death penalty in the USSR in 1937-1938) for the entire Soviet rule (1917-1990), of which the majority of executions happened in 1937-1938.
Here is the report by Ministry of Internal Affairs made in December 1953 for the period 1921-1938. The ВМН column means executions.
Everything else can be attributed to Stalin only indirectly.
The Western and anti-Soviet propaganda (e.g, Black Book of Communism) usually attributes to Stalin
The famine in Ukraine. The archival sources show that the famine could bring about 2 million death, in Western propaganda this number exaggerated a lot. Western propaganda also makes a "genocide of Ukrainians" from this famine, despite evidence such as Stalin's correspondence that shows that Stalin was actively investigating the causes of the famine and took measures. Other anti-Soviet sources just blame Stalin for criminal negligence or call the famine an outcome of collectivization.
The number of casualties in World War II. The western propaganda usually blames Stalin for too high casualties in the initial period of the war as well as often blames him for not predicting the German invasion well and/or blindly cooperating with Germany. Military casualties are usually intentionally mixed with civilian ones so to inflate numbers. So for all people dead due to Nazi genocide Stalin is blamed. He is also accused for shortages of the equipment in the military which allegedly led to higher casualties.
The hunger deaths during the siege of Leningrad. The propaganda usually blames Stalin for refusing to evacuate the city.
The number of people dead in prisons. Stalin ruled for a long period of time, so during his rule about 2 million people died in prisons. Statistics indicate that death rate in prisons under Stalin with exception of the years of war was not much different from deaths in modern Russia or other countries and was even smaller than the death rate among the general piopulation (this is because among the imprisoned were mostly young strong people). The total number of inprisoned was smaller per person than in modern USA and slightly greater than in modern Russia.
Some sources (e.g. Dyadkin, “Unnatural Deaths in the U.S.S.R.: 1928-1954,”) go as far as to projecting the Imperial Russia's pre-revolutionary demographics on to Soviet time and estomating the population numbers that would be expected if the trend continued so to blame the difference in the population numbers on the Stalin's mismanagement or cruelty.
A notable piece of propaganda is the book "Europe. A History." by Norman Davies (1996).
Here is the page where he gives the estimates of "the number of people killed in Soviet Russia and the Soviet Union 1917-1953 (excluding the losses 1939-1945)". He claims the estimates are after R. Medvedev and R.Conquest, the both sources from mid-1960s when Soviet archves were not yet available. Nevertheless, Davies arrives at the number more than twice that of Modvedev or Conquest each.
To see how ridiculous these numbers of "killed" are, lets consider the "deportations to Gulag".
According the report to Khrushchev of 01.02.1954 (you can see the full text at the site of N.Yakolev's foundation, a very anti-Stalinist and anti-Soviet institution).
the total number of the convicted 1921-1954 was approximately 3 777 000. Of which 765 180 convicted for counter-revolutionary crimes were sentenced to excile or deportation abroad. Also (according the prevuous report) at least 745 000 were executed. This leaves 2 660 000 sentenced to imprisonment (of which only a part were sent to Gulag). Well according to Davis, during the deportation to Gulag were killed 17 million. Apparently some people were killed up to 10 times!
Moreover, the average death rate in Gulag is also well known from the archive data:
Sources: Zemskov V.N. Gulag. Sociological research. 1991. #6 pp.14-15; for 1931-1940 - ГАРФ (Russian state archive), ф.9414, оп.1, д.1155, л.2; д.2740, л.1, 5, 8, 14, 26, 38, 42, 48, 58, 96-110
Note also that many who died during the war died not due to maltreatment but because they volunteered to the front (that would reduce the term of their sentence).