Days recommended to fast.

Mondays / Thursdays

Abu Hurairah (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said, "Deeds of people are presented (to Allah) on Mondays and Thursdays. So I like that my actions be presented while I am fasting.''
[At-Tirmidhi].

Three "Bright" Days of Each Month

`Abdullah bin `Amr bin Al-`As (May Allah be pleased with them) reported: The Messenger of Allah (PBUH) said, "Observing Saum (fasting) on three days of every month is equivalent to a full month's fasting.''
[Al-Bukhari and Muslim].

Abu Dharr (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said, "If you want to observe Saum on three days in a month, then fast on the thirteenth, fourteenth and fifteenth of the (lunar) month.''
[At-Tirmidhi].