There's several ahadith where Prophet Muhammad ordered people to be killed for crimes. As for having the wrong religion:
Prophet Muhammad directly ordered some apostates to be killed, e.g. Sahih Muslim 1671 a.
Prophet Muhammad is considered to have killed in battle, yet strongly objected to killing someone after they said There is no god but Allah (Sahih Muslim 96 a). They could have been spared had they converted to Islam, like some people who were spared beheading at Banu Qurayza.
I did not find an example of Prophet Muhammad killing someone himself solely for having the wrong religion (despite searching the Islam-critical site WikiIslam.net's list). Most records are of Prophet Muhammad ordering people to be killed. However, Prophet Muhammad is recorded as killing people for other crimes. For example: The Prophet killed a Jew for killing a girl in order to take her ornaments (Sahih al-Bukhari 6885).
The line is a bit blurry when it comes to Islamic battles which include religious motivations. Some examples of these are Prophet Muhammad and the Battle of Badr and Conquest of Mecca (see also List of expeditions of Muhammad on Wikipedia).
Other Prophets are not reported to have engaged in fighting as much. This is what I'm aware of:
Prophet Dawud killed Goliath in battle (Qur'an 2:251).
Prophet Musa killed a man (before prophethood):
And he entered the city at a time of inattention by its people and found therein two men fighting: one from his faction and one from among his enemy. And the one from his faction called for help to him against the one from his enemy, so Moses struck him and [unintentionally] killed him. [Moses] said, "This is from the work of Satan. Indeed, he is a manifest, misleading enemy."
IslamWeb describes it as accidental (as does the Sahih International translation).
Prophet Ibrahim attempted to sacrifice his son, but he was saved.
Prophet Sulayman was prepared for war with the Queen of Sheba, but she accepted Islam.
Prophet Job made an oath that he would beat his wife with 100 strokes, although Allah gave him a way to uphold the oath by lightly beating her: ...take in your hand a bunch [of grass] and strike with it and do not break your oath... (Qur'an 38:44).
Prophet Musa, thinking that his brother Harun allowed idol worshipping, ...seized his brother by [the hair of] his head, pulling him toward him... (Qur'an 7:150).
Some of the Prophets' warnings were ignored, which resulted in Allah killing them: Prophet Lut, Prophet Nuh, Prophet Hud, Prophet Shuaib, and Prophet Saleh. There's also Prophet Musa and the parting of the seas (Qur'an 26:63-66), where the pursuers were drowned.