I never saw the Prophet (ﷺ) laughing to an extent that one could see his palate, but he always used to
smile only.
Sahih al-Bukhari Book 78, Hadith 119
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Um Sulaim said, "O Allah's Messenger (ﷺ)! Verily Allah is not shy of (telling you) the truth. Is it essential for a woman to take a bath after she had a wet dream (nocturnal sexual discharge)?" He said, "Yes, if she notices discharge. On that Um Salama laughed and said, "Does a woman get a (nocturnal sexual) discharge?" He said, "How then does (her) son resemble her (his mother)?"
Sahih al-Bukhari Book 78, Hadith 118 Next Hadith → A man came to the Prophet (ﷺ) on a Friday while he (the Prophet) was delivering a sermon at Medina, and said, "There is lack of rain, so please invoke your Lord to bless us with the rain." The Prophet (ﷺ) looked at the sky when no cloud could be detected. Then he invoked Allah for rain. Clouds started gathering together and it rained till the Medina valleys started flowing with water. It continued raining till the next Friday. Then that man (or some other man) stood up while the Prophet (ﷺ) was delivering the Friday sermon, and said, "We are drowned; Please invoke your Lord to withhold it (rain) from us" The Prophet smiled and said twice or thrice, "O Allah! Please let it rain round about us and not upon us." The clouds started dispersing over Medina to the right and to the left, and it rained round about Medina and not upon Medina. Allah showed them (the people) the miracle of His Prophet and His response to his invocation.
Sahih al-Bukhari Book 78, Hadith 120
Sahih al-Bukhari Book 78, Hadith 118 Next Hadith → A man came to the Prophet (ﷺ) on a Friday while he (the Prophet) was delivering a sermon at Medina, and said, "There is lack of rain, so please invoke your Lord to bless us with the rain." The Prophet (ﷺ) looked at the sky when no cloud could be detected. Then he invoked Allah for rain. Clouds started gathering together and it rained till the Medina valleys started flowing with water. It continued raining till the next Friday. Then that man (or some other man) stood up while the Prophet (ﷺ) was delivering the Friday sermon, and said, "We are drowned; Please invoke your Lord to withhold it (rain) from us" The Prophet smiled and said twice or thrice, "O Allah! Please let it rain round about us and not upon us." The clouds started dispersing over Medina to the right and to the left, and it rained round about Medina and not upon Medina. Allah showed them (the people) the miracle of His Prophet and His response to his invocation.
Sahih al-Bukhari Book 78, Hadith 120