Halal Haircuts in Islam
Question

What was the hairstyle of the Prophet (peace and blessings of Allah be upon him)? And what hairstyles are disallowed specifically?
Praise be to Allah.Hairstyle of Prophet Muhammad (peace and blessings of Allah be upon him)
The hairstyle of the Prophet (peace and blessings of Allah be upon him) is mentioned in a number of hadiths, such as the following: 

His hair was neither curly nor straight. 

Anas ibn Malik (may Allah be pleased with him) said, describing the Prophet (peace and blessings of Allah be upon him), he was of average height, neither very tall nor very short . He had a ruddy complexion, neither very white nor very dark, and his hair was neither curly nor straight. The revelation came to him when he was forty years old.  (Narrated by al-Bukhari, 3354; Muslim, 2338) 

His hair came down to his earlobes. 

Al-Bara ibn ‘Azib (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) was of average height and broad shouldered. He had hair that came down to his earlobes. I saw him wearing a red garment and I never saw anyone more handsome than him. (Narrated by al-Bukhari, 3358; Muslim, 2337) 

His hair sometimes came down to his shoulders. 

Qatadah said: I asked Anas ibn Malik (may Allah be pleased with him) about the hair of the Messenger of Allah (peace and blessings of Allah be upon him). He said, “The hair of the Messenger of Allah (peace and blessings of Allah be upon him) was neither curly nor straight, and came down to a point between his ears and his shoulders.” (Narrated by al-Bukhari, 5565; Muslim, 2337)
According to another report, his hair used to touch his shoulders. (Narrated by al-Bukhari, 5563; Muslim, 2338)
Sometimes his hair was shorter than that. All of this may be understood as referring to different situations, and each of the Companions narrated what he had seen. 

The Prophet (peace and blessings of Allah be upon him) used to dye his hair sometimes. 

‘Uthman ibn ‘Abd-Allah ibn Muhib said: I entered upon Umm Salamah and she brought out to us one of the hairs of the Prophet (peace and blessings of Allah be upon him) which was dyed. (Narrated by al-Bukhari, 5558) 
Ahmad (25328) added: “… dyed with henna and katam.” 
Katam is a plant that is used to dye hair. When mixed with henna, it gives the hair a colour between black and red. (See ‘Awn al-Ma’bud, commentary on hadith no. 4205)

He used to part his hair. 

‘Ibn ‘Abbas (may Allah be pleased with him) narrated that the Messenger of Allah (peace and blessings of Allah be upon him) used to let his hair hang down over his forehead and the pagans used to part their hair, and the People of the Book used to let their hair hang down over their foreheads. The Messenger of Allah (peace and blessings of Allah be upon him) liked to be like the People of the Book in matters where there was no specific command. Then the Messenger of Allah (peace and blessings of Allah be upon him) parted his hair. ((Narrated by al-Bukhari, 3365; Muslim, 2336).
Some of the scholars discussed the meaning of this hadith, and their comments were summed up by Imam al-Nawawi as follows: 
The correct view is that both letting the hair hang down over the forehead and parting it are permissible, but that parting is better. (Sharh Muslim, 15/90) 

The Prophet (peace and blessings of Allah be upon him) did his Farewell Pilgrimage when his hair was stuck together. 

(This means) making some parts of the hair stick to others using gum or something similar, so that the hair is held together and avoids getting dirty and does not need to be washed. This is easier for the person who is in ihram, especially in the past when the person in ihram was faced with a lot of dirt and little water. 
Ibn ‘Umar (may Allah be pleased with him) said: I saw the Messenger of Allah (peace and blessings of Allah be upon him) raising his voice in the Talbiyah, with his hair stuck together. (Narrated by al-Bukhari, 5570; Muslim, 1184)

The Prophet (peace and blessings of Allah be upon him) sometimes used to braid his hair, especially when travelling, to keep it from getting dusty. 

Umm Hani said: “The Prophet (peace and blessings of Allah be upon him) came from Makkah with four braids.” (Narrated by al-Tirmidhi, 1781; Abu Dawud, 4191; Ibn Majah, 3631. Classed as sahih by al-Hafiz Ibn Hajar in Fath al-Bari, 10/360” 
Halal haircuts in Islam
With regard to the kinds of hairstyles that are forbidden, they are characterized by the following:                                                                                                  

Al-Qaza’ (lit. tufts), which is where part of the head is shaved and part is left. 

Ibn ‘Umar narrated that the Messenger of Allah (peace and blessings of Allah be upon him) forbade al-qaza’. (Narrated by al-Bukhari, 5466; Muslim, 3959) 
One of the narrators of this hadith defines al-qaza’ as shaving part of a child’s head and leaving some of his hair. 
Ibn al-Qayyim (may Allah have mercy on him) said: 
“With regard to shaving part of the head and leaving part , this is of varying degrees. 
The worst is shaving the middle of the head and leaving the sides, as the Christian monks do. 
After that comes shaving the sides and leaving the middle, as many of the foolish and worthless people do. 
After that comes shaving the front of the head and leaving the back. 
These three types all come under the heading of qaza’ which was forbidden by the Messenger of Allah (peace and blessings of Allah be upon him), but some of them are worse than others.” (Ahkam Ahl al-Dhimmah, 3/1294) 

Imitating the unbelievers or immoral people. 

There are many such hairstyles, some of which come under the heading of qaza’ – such as the “Marines” haircut, which is forbidden for two reasons, the fact that it is a kind of qaza’ and the fact that it is an imitation of the unbelievers . Some of them do not involve qaza’ but they are styles that belong to the unbelievers, such as making some of the hair stand up and letting the rest hang down, and so on. 
This also includes every hairstyle that belongs to the unbelievers or immoral people, because it is not permissible for a Muslim to resemble them in that, because the Prophet (peace and blessings of Allah be upon him) said, “Whoever imitates a people is one of them.” (Narrated by Abu Dawud, 4031. Classed as hasan by al-Hafiz ibn Hajar in Fath al-Bari, 10/271. its isnad was classed as jayyid by Shaykh al-Islam in Iqtida al-Sirat al-Mustaqim, p. 82) 
Shaykh al-Islam said: 
“The least that we can say about this hadith is that it implies that it is haram to imitate them, although the apparent meaning is that the one who imitates them is a kafir, as in the verse (interpretation of the meaning): 
“And if any amongst you takes them (as Awliya), then surely, he is one of them.” [al-Maidah 5:51]” (Iqtida al-Sirat al-Mustaqim, p. 83)

Imitating foolish people. 

These are hairstyles worn by some of the foolish people, which may be included in the categories mentioned above. 
And Allah knows best.