There are many, many, many groups that all say they are Christian yet they have such differing views on what that is that they will not worship together. Is Islam the same? Roughly, how many groups of Islam are there that will not worship with other groups? Are some of them hostile or violent to each other like the Catholics and Protestants in N. Ireland?
I will start by quoting this hadith :
Narrated AbuHurayrah: The Prophet (PBUH) said:
The Jews were split up into seventy-one or seventy-two sects; and the Christians were split up into seventy one or seventy-two sects; and my community will be split up into seventy-three sects.
As you can see the prophet already said that Islam will also split into too many sects. Such as Sunni,shiite,Abadthi etc...
However the most dominant is the sunnis (~90% of muslims) and then followed by the shiite (~10% of the muslim population) and the rest is divided between other sects.
Anyone of these sects can be a hostile sect if they want. There is not sect that encourages its followers to be hostile. But its the followers who take advantage of their sect to start attacking others.
For example, some Sunnis may create a group called X and this group will start attacking Y hence Y will start blaming the sunnis because X belong to the sunni sect.
I hope this simple answer would give you some idea about the groups in Islam
As Suhaib said, the major divisions are Sunni and Shiia. Sufism is sometimes considered another division, but some Sufis identify as being Sunni or Shiite. Different schools of thought also exist within those divisions, however it does not interfere with followers worshiping together. There are also some groups who identify as Muslim or include Islamic tradition but are not included in the greater Muslim community.
There's a brief history of the divisions and schools of thought on the New World Encyclopedia.
The divisions of Islam differ greatly from those of Christianity in that followers are unified in their obligation to perform a pilgrimage (hajj) to Mecca. Despite sectarian conflict, the Saudi government grants visas to pilgrims from countries who would not typically be allowed into the country. Sectarian conflict began in the division between Sunni and Shiia (a brief account can be found in the previous link), and continues today. Although it is integrated in political strife, there are sectarian debates in Saudi/Iranian relations, civil conflicts in the Gulf countries, and the war in Syria, to name a few. The hajj is sometimes disrupted by sectarian conflict, but the intention is to unify Muslims from around the world.
It's rather difficult to answer this one, so keep in mind that this answer might be anecdotal and based on personal experience.
As with any large enough religion, much of the fragmentation is political and cultural. Few are strictly religious. Tolerance varies across the board.
There are far too many small sects that are considered cults by some people. In my country, some people of different political parties refuse to pray in the same mosque, both accusing the other of being heretics.
Sunni and Shia' may often avoid praying in the same location. Tolerance varies from brotherly hugs to awkward stares to outright bombings. Sufis are generally tolerant of others, but many (yet not most) do not tolerate them, even the ones whose ancestors converted to Islam because of the action of Sufi missionaries.
Some groups do not acknowledge the Hadiths (narrations) of the Prophet at all and will outright reject them. Some groups follow Hadiths to the letter, whereas some take it as mere advice. Some people use a Hadith-based law before Quranic law. Some people recognize a Hadith as strictly being something from the Prophet Muhammad SAWS, whereas others recognize anything by his companions as Hadiths, and any laws dispensed by them as Islamic law.
The more conservative groups will reject other Abrahamic religions, whereas some Muslims will consider other Abrahamic religions (including the Bible and Torah) to be from Allah. To get a general feel of it, while other Muslims see each other as 'brothers', they see Christians/Jews as 'cousins', and Sunni/Shia' as the disowned brother of the family. Note that mileage varies strongly by area and culture.
If you want to go into the politics, a lot of the people who claim Islamic unity care little about Muslims as a whole; many utilize Islam as a political cause. Many 'jihadists' will kill a fellow Muslim as well. There was an insurgency in my country recently, in which both sides of the conflict were Muslims and killing Muslims, but were spreading propaganda that anyone who died in that conflict were martyrs (as in dying in the cause of Allah).
On the other scale of tolerance, there are mosques which allows Buddhists, Christians, and other non-Muslims to utilize the mosque area for meditations and prayer.