|"With ten trials did our ancestors test the Holy One, blessed be He, in the desert, as it is stated, ‘They have tested Me these ten times and did not hearken to My voice’ (Numbers 14:22)."
The Talmud (Erchin 15a) contains a similar statement to our mishna and enumerates the ten trials. They are as follows:
(1) The Children of Israel, pinned against the Red Sea with the Egyptians in close pursuit, complained to Moses: "Was it for a lack of graves in Egypt that you took us to die in the desert?" (Exodus 14:11).
(2) After safely crossing the Sea, Israel suspected that the Egyptians ascended on the opposite bank — until G-d had the water spit them out.
(3) Complaining for water at Marah (ibid., 15:24).
(4) Complaining for food at the Desert of Sean (ibid., 16:2-3).
(5) Leaving over Manna — in defiance of the command not to leave the Manna overnight (16:20).
(6) Searching for Manna on the morning of the Sabbath (v. 27).
(7) Complaining for water at Refidim (17:1-3).
(8) The sin of the Golden Calf (32:1-6).
(9) The "mixed multitude" of nations which accompanied Israel complaining for meat, precipitating Israel’s complaining as well (Numbers 11:4-6).
(10) The sin of the Ten Spies (who returned from spying the Land of Israel with a negative report) (ibid., Ch. 13-14). At this final trial, G-d refers to Israel as "having tested Me these ten times," as quoted in our mishna.