Orcs and Humans : The demon-corrupted Orcs destroyed many Human settlements and killed many Humans. When the Burning Legion was defeated, the surviving Orcs were put into concentration camps and were treated as slaves until their liberation/escape to Kalimdor.
Trolls and Humans: Trolls and Humans have been fighting territorial wars since the beginning of their shared histories.
Night Elves and Orcs: When the Orcs came to Kalimandor, a group of them started logging a portion of Ashenvale and fought and killed Cenarius, a defender of the forests there.
Blood Elves and Humans: the Blood Elves were abandoned by the Human-led Alliance to the Scourge and the surviving Blood Elves shunned by the Alliance.
Forsaken and Humans: the Humans cannot or will not differentiate between the Forsaken and the Scourge. When many of the Forsaken tried to contact their families, they were shunned and scorned by both their society and their church. Afterwards, they started calling themselves the Forsaken, because they were forsaken by both family and the Light.
Tauren and Humans and Night Elves: many Humans and Night Elves look down on the Tauren as brutish and bestial, even though the Tauren are actually peaceful and contemplative.
Tauren and Dwarves: some Dwarves have been mining/digging in Tauren land, disregarding Tauren sensitivities. The Dwarves also destroyed and/or drove out the Tauren settlers who were living in one of their digsites.
Draenei and Orcs: the demon-corrupted Orcs killed many Draenei under the influence of the Burning Legion in Draenor, the Orcs' homeworld.
Blood Elves and Draenei: there might be some bad blood as Kael'thas Sunstrider, prince of the Blood Elves, sent some Blood Elf spies to destroy the Draenei who crashed there.
And there are many atrocities done by both sides during the previous wars.