Allah, the Wise, has said:
إِنَّ ذٌالِکُمْ کَانَ يُؤْذِي النَّبِيَّ فَيَسْـتَحْيِي مِنْکُمْ وَ اللٌّهُ لاَ يَسْتَحْــيِ مِنَ الْحَقِّ
"Such (behaviour) annoys the Prophet: he is ashamed to dismiss you, but Allah is not ashamed (to tell you) the truth." 
The Noble Prophet (sa) said:
أَلْحَياَءُ خَيْرٌ کُلُّهُ
"Every kind of modesty is goodness." 
Modesty is a luminosity, the essence of which is faith, and therefore, modesty stems from faith and ought to be strengthened by means of it.
A person who possesses modesty enjoys every kind of goodness - restraining himself in the face of every repugnant and impure act - but one who lacks modesty and shame, acquires every kind of evil, although he may appear to engage himself in acts of worship. A person who lacks this virtue shall be left deprived (of mercy) and will be afflicted with the punishment of the Hereafter. Modesty, in the initial stage, transforms into 'fear of Allah', while in the final stage, into 'perception of Allah'.
A person who is in possession of this virtue, is heedful of Allah, distant from sins and disobediences, and cloaked with honour and love.
1 – Musa and the Daughters of Shuaaib
When Musa (as) killed the person from Qabt, the followers of Firaawn schemed to have him murdered, and so he fled from Egypt. After travelling for between three and eight days and enduring great troubles, he reached the city of Madyan, where he stretched out to rest beneath a tree situated near a well.
He realized that there were two ladies standing near the well, waiting for the shepherds to finish drawing water so they too could draw water from the well. He went to them and offered to help by drawing the water for them. As a result of Musa's help, the women brought the water home sooner than usual and this prompted their father, Shoaaib (as) to inquire: "How did you manage to bring the water sooner than usual today?"
They narrated to him the entire episode, whereupon Sho'aib said, "Go to the man and bring him to me in order that I may reward him for his act."
The ladies approached Musa (as). As soon as they conveyed their father's message to him, he immediately agreed, as he was hungry, tired and a stranger in the place. The maidens led the way while Musa (as) followed them, but as they walked, the outlines of their bodies became visible and this appeared unsuitable to Musa's modesty (to look at). Consequently, he said to them: "I shall lead the way while you follow up behind me; correct me if you find me heading in the wrong direction (or throw pebbles before me so that I know where to go) for we, the children of Yaaqub, do not look at the backs of women."
When the ladies approached Shoaaib (as) and related the incident to him, he gave his daughter in marriage to Musa (as), owing to the latter's assistance, modesty, purity, trustworthiness and physical strength.
2 – The Modesty of the Eyes
It has been related in the commentary Ruhul Bayan that in a city there lived three brothers. The eldest brother had been the muezzin of the mosque in the city and used to recite the adhan from the top of its minaret. After extending his services for ten years, he died and the second brother took over his brother's task. A few years later, this brother died too and so, the people approached the third brother and urged him to accept this responsibility and not to let the sound of adhan be terminated. But he flatly refused.
"We shall give you a large amount of money!" they said to him.
But he replied, "Even if you were to give me a hundred times more, I would not accept this task."
"Is the recitation of adhan an evil act?" they asked him.
"No, but I shall not recite it from the top of the minaret."
When they sought to know the reason for his refusal, he said, "This minaret is a place that has caused my two wretched brothers to die without faith. I was near my eldest brother when he was breathing his last and I desired to recite the Surat Yasin to ease the agony of his death, but he prohibited me from reciting it.
"The second brother too departed from the world in the same manner. In order to know the reason for this problem, Allah graced me and I saw my eldest brother in my dream, in a state of chastisement. I said to him: 'I shall not leave you till you tell me what caused both of you to die without faith?' He said: 'Whenever we ascended the minaret, we would look at the womenfolk in the people's houses, without shame and modesty. This act of ours used to engage our hearts and occupy our thoughts, leaving us neglectful and heedless of Allah, and this is what has caused us to become wretched and earned for us an evil Hereafter.'"
3 – Zulaikha
When Zulaikha followed Yusuf to gratify herself and proposed to commit the sin, Yusuf suddenly observed that she had covered something with a piece of cloth.
"What did you do?" he asked her.
"I have covered the face of the idol so that it does not watch me while I commit the sin," she replied.
Hearing this, Yusuf said, "(If) you exhibit shyness and modesty before a stone that does not see, it is more befitting for me to exhibit shame and modesty before the One, Who sees and Who is aware of what is manifest about me and what is concealed within me."
4 – The Modesty of Amirul Moaminin
The marriage formula between Imam Ali (as) and Hadhrat Zahra had been recited in the year 2 ah, but the wedding ceremony took place only later (after one month or one year, as per varying reports).
During this period, Ali (as), out of shyness, would not utter the name of Fatimah and she too behaved likewise.
This continued till one day, the wives of the Noble Prophet (sa) approached Ali (as) and asked: "Why do you delay the wedding ceremony? If you experience a feeling of shyness and timidity, permit us to speak to the Noble Prophet (sa) about it." Imam Ali (as) granted them permission.
En masse, they arrived in the presence of the Noble Prophet (sa).
"O' Prophet of Allah!" they said. "Had Khadijah been alive, Fatimah's wedding ceremony would have left her overjoyed and Fatimah herself would be happy to set her eyes upon her husband. Ali (as) too awaits his wife and we look forward to this joyous occasion."
Hearing Khadijah's name, tears welled up in the Noble Prophet's eyes. With a heave of sigh, he said, "Where is there the like of Khadijah…?" and then added, "But why did Ali (as) not approach me directly for this?"
The wives replied, "His modesty restrained him from doing so."
Hearing this, the Noble Prophet (sa) directed them to make preparations for the wedding ceremony.
 Noble Qur'an, Suratul Ahzab (33), Verse 53
 Jamea al-Saaadat, Volume 2, Page 385
 Tadhkeratul Haqaiq, Page 93
 Tarikh-e-Anbiya, Volume 2, Page 65-71
 Riwayat-ha Wa Hikayat-ha, Page 105; Dastan-ha-e-Parakandeh, Volume 1, Page 123
 Namunah-e-Maaarif, Volume 4, Page 385; Bahrul Mahajjah (of Ghazzali), Page 94
 Fatimah al-Zahra, Page 283