Voluntary Fasting

The fasting of Ramadan is obligatory on every responsible and fit Muslim (Mukallaf). But there are other times when it is strongly recommended, As Prophet Muhammad (peace be on him) used to do. Among these times are Mondays and Thursdays of every week, a few days of each month in the two months heralding the coming of Ramadan, i.e., Rajab and Sha'ban, six days after Ramadan following the 'Eidul-fitr day. Besides, it is always compensating to fast any day of any month of the year, except the 'Eid days and certain days when no Muslim should fast. However, we may repeat that the only obligatory fasting is that of Ramadan.

The Prophet (peace be on him) used to encourage fasting in the following days:

Six days in Shawwal ( the month after Ramadan); the Prophet (peace be on him) said: «Whoever fasts Ramadan, then follows it up with six days in Shawwal, it is as if he fasted the whole (year).» [Reported by Muslim]
«من صام رمضان. ثم أتبعه ستا من شوال. كان كصيام الدهر»

The scholars said that the reward of the good deeds are multiplied by ten. 30X10= 300 + [6 days x 10] = 360 which is slightly longer than a lunar year, and next Ramadan he will fast again so it is as if he fasted his whole life.

Fasting the first ten days of Dhul-Hijjah and the day of 'Arafah (the 9th day of Dhul-Hijjah) (for those who are not performing Hajj); the Prophet (peace be on him) said: «Fasting on the day of 'Arafah expiates two years of sins last year's and next year's and fasting on the tenth of Muharram ('Ashura) expiates the previous year's (of sins).» [Reported by Muslim]
«صيام يوم عرفة، أحتسب على الله أن يكفر السنة التي قبله. والسنة التي بعده. وصيام يوم عاشوراء، أحتسب على الله أن يكفر السنة التي قبله»

«Milk was sent to the Prophet (peace be on him) while he was giving his sermon on the day of Arafah and he drank from it.» [Reported by Ibn Gareer Al Tabari]
«عن ابن عباس قال أرسلتني أم الفضل إلى النبي صلى الله عليه وسلم بلبن وهو يخطب الناس يوم عرفة فشربه »

«Fasting on the day of 'Ashura, and its fasting is not mandatory on you, and I am fasting, so whoever wants should fast, and whoever wants should break his fast.» [Reported by Bukhari]
«هذا يوم عاشوراء ، ولم يكتب عليكم صيامه ، وأنا صائم ، فمن شاء فليصم ومن شاء فليفطر»

And he (peace be on him) said: «If I live till the next year, I will fast definitely on the 9th ( the day before "Ashura).» [Reported by Muslim]
«لئن بقيت إلى قابل لأصومن التاسع»
(This shows that it is preferable to fast an extra day long with the tenth, preferably the ninth, but, if not possible, then the 11th).

Fasting most of the month of Sha'ban.
«Allah's Messenger (peace be on him) used to fast most of Sha'ban.» [Reported by Bukhari]
«وما رأيته أكثر صياما منه في شعبان»

Fasting Monday and Thursday. The Prophet (peace be on him) mentioned that: «The deeds of the worshippers are presented before Allah on Monday and Thursday, I like my deeds to be presented while I am fasting.» [Reported as Saheeh by Albani]
«إن الأعمال ترفع يوم الاثنين و الخميس، فأحب أن يرفع عملي و أنا صائم »

He (peace be on him) was asked about fasting on Monday, he said: «That is the day I was born and the day (the first Revelation) was sent down on me.» [Reported by Muslim]
«"-وسئل عن صوم الاثنين؟ قال "ذاك يوم ولدت فيه. ويوم بعثت -أو أنزل علي فيه »

Days Taboo for Fasting:

It is taboo to fast during the first days of Eid Al-Fitr and Eid- Al-Adha in compliance with the directive of the Prophet (peace be on him): «The Prophet peace be upon him has forbidden fasting the day of Fitr and the day of Adha». [Reported by Muslim]
«أن رسول الله صلى الله عليه وسلم نهى عن صيام يومين: يوم الأضحى ويوم الفطر»

Undesirable Days of Fasting:

The Legislator has advised Muslims not to fast on certain days and explained the reasons and wisdom behind the exhortation. These days are:

The days of the Tashrik, the three days following the Feast of the Sacrifice, Abu Huraira (May Allah bless him) related that the Apostle (peace be on him) had delegated Abdullah Bin Huzakah to tour throughout Mina and to advise Muslims not to fast during these three days which had been assigned for eating, drinking and mentioning of the name of Allah.
Specific fasting of Friday, the Muslim weekly holiday, if not preceded or followed by another day is undesirable but not taboo. In the two Hadith Books checked properly by well versed jurist and scholars, Amer (May Allah bless him) related that the Prophet (peace be on him) said"«Friday is your Eid, do not fast on it if not preceded or followed by another day». [Reported by Al Haithami as Isnadoh Hassan]
«إن يوم الجمعة عيدكم فلا تصوموه إلا أن تصوموا قبله أو بعده»

Fasting on Saturday is undesirable because this is glorified by the Jews.
It is preferable for a pilgrim not to observe Saum (fast) on the day of 'Arafah in 'Arfat.

Narrated Umm Al-Fadl bint Al-Harith (May Allah bless her): «On the day of 'Arafah, some people who were with me, differed about the Saum (fast) of the Prophet (peace be on him); some said that he was observing Saum while others said that he was not observing Saum. So I sent a bowl full of milk to him while he was riding his camel, and he drank that milk.» [Reported by Bukhari]
«أن ناسا تماروا عندها يوم عرفة في صوم النبي صلى الله عليه وسلم، فقال بعضهم: هو صائم ، وقال بعضهم: ليس بصائم، فأرسلت إليه بقدح لبن، وهو واقف على بعيره، فشربه.»

Source: http://www.al-islam.com
By few modifications.