"The observance of three days' fast every month and that of Ramadan every year is a perpetual fasting. I seek from Allah that fasting on the day of Arafah may atone for the sins of the preceding and the coming years, and I seek from Allah that fasting on the day of Ashura may atone for the sins of the preceding year."

- Sahih Muslim

When Allah's Messenger (sallallaahu 'alaihi wasallam) came to Medina, he found the jews fasting on the day of 'Ashura' (i.e. 10th of Muharram). They used to say: "This is a great day on which Allah saved Moses and drowned the folk of Pharaoh. Moses observed the fast on this day, as a sign of gratitude to Allah."
The Prophet said, "I am closer to Moses than they." So, he observed the fast (on that day) and ordered the Muslims to fast on it.

- Sahih Bukhari

'Beware of suspicion (about others) as suspicion is the falsest talk,
and do not spy upon each other,
and do not listen to the evil talk of the people about others' affairs,
and do not have enmity with one another, but be brothers.
And none should ask for the hand of a girl who is already engaged to his (Muslim) brother, but one should wait till the first suitor marries her or leaves her.'

- Sahih Bukhari