1. Hanuman
Valmiki Ramayana 5.35.1-9
Then, seeing Hanuma, who was tawny coloured like a series of flashing thunderbolts wrapped up in a white cloth and hiding behind the branches of a tree, Seetha had her mind shaken…Seetha got a great surprise and thought (as follows): “Alas! This monkey is hard to be approached, fearful and difficult to be looked at.” Thus thinking, she was bewildered again. The splendid woman Seetha, bewildered by fear and afflicted with grief, lamented most piteously saying “0, Rama! 0, Rama! and “O Lakshmana!”. Seetha wept faintly in a low voice in many ways. Seeing that excellent monkey appraching humbly, that splendid woman Seetha thought it as a dream… As soon as seeing Hanuma Seetha lost her consciousness very much and became seemingly lifeless. Regaining her consciousness after a long time the wide a eyed Seetha moreover thought (as follows), Today, I saw an ugly monkey, in my dream, which is forbidden according to a body of scriptures. May it be well with Rama together with Lakshmana and with my father, King Janaka.” (source)
2. Ram
Valmiki Ramayana 2.34.1
Thereafter, the lotus-eyes Rama, who was dark-brown in complexion and great beyond compare, spoke thus to the charioteer, “Tell about me to my father.” (source)
Valmiki Ramayana 5.35.16
He has a voice like the sound of a kettle-drum. He has a shining skin. He is full of splendour. He is square-built. His limbs are built symmetrically. He is endowed with a dark-brown complexion.” (source)
3. Shiva
Shrimad Bhagavatam 4.2.12-15
He has eyes like a monkey’s, yet he has married my daughter, whose eyes are just like those of a deer cub. Nevertheless he did not stand up to receive me, nor did he think it fit to welcome me with sweet words. Shiva lives in filthy places like crematoriums, and his companions are the ghosts and demons. Naked like madman, sometimes laughing and sometimes crying, he (shiva) smears crematorium ashes all over his body. He (shiva) does not bath regularly, and he ornaments his body with a garland of skulls and bones.” (source)
Narada Purana 3.79.220-225
The garland of hellish things is your ornament for the chest. The poisonous serpents viz. Vasuki and Sesa are your bangles. Your garments are the quarters (i.e. you are naked); the matted hair is what you have by way of your tresses. The white ash constitutes your unguent, the great bull is your vehicle. Your Gotra (spiritual lineage) and the family are not known. Your parents are unknown, your body is rendered ugly with hideous eyes. Even as the daughter of the mountain was saying this Visnu spoke to her angrily. ‘O goddess, why do you censure our lord of the universe, the lord of Devas. O gentle lady due to your nature of not controlling yourself you were not his beloved. You are like the evil vital breaths. O gentle lady, it is my vow that I shall die where Isa is censured.’ After saying this, Hari attempted to cut off his head. Mahesa caught hold of his hand and said, ‘Do not indulge in a risky venture. Everything that Parvati said is pleasing to me not displeasinag” (source)
Linga Purana 1.31.28-32
The lord had vulgar traits. He was stark nude. He had smeared his limbs with ashes. His hands were engaged in whirling a firebrand. His eyes were red and tawny. Sometimes he laughed boisterously, sometimes he sang surprisingly. Sometimes he danced amorously and sometimes he cried repeatedly. He roamed round the hermitages and begged for alms. He assumed forms of his choice by his Maya…” (source)
Matsya Purana 154.329-341
Hearing those words the sages controlling their mind and realizing her object said:- “Daughter! There are two kinds of comforts in the world and the first one is the gratification of the body; the second is the peace of mind. Lord Siva is, by nature naked, ferocious, Dweller of the cremation ground, the carrier of skulls, a hermit, statue like in action, a beggar, mad, fond of collecting ugly and terrible things, and inauspiciousness incarnate. What advantage will you get in having him as your husband…” (source)