Is it permissable to say “yemach shemo” on any goy or only on those who are known to have harmed the Jewish people.
There are several precedents in Chazal for behaving in a mannered and polite was towards non-Jews (see Berachos 17a). This is not only because of the need to put on a ‘good showing’, but rather because of the requirement to behave in a refined and respectable manner at all times. A major part of this behavior is the way in which we speak, and it is certainly wrong to say yemach shemo about any human being, provided he is not a truly wicked person who we desire should be wiped off the face of the world.
It should be added that even prior to reaching arguments of morality and ethics, the Torah in general does not wish anyone but the wicked to be destroyed. Our prayers for the glory of future times include non-Jews (such as the prayer for Rosh Hashanah and Yom Kippur), speaking of ‘all occupants of the world’ that will know Hashem. In the same prayer, it is only sin and iniquity that is doomed to perish in smoke, and certainly not all non-Jews.
Those who use the term yemach shemo freely should be admonished.