To appease the Night Mother and Sithis, I think. That seems to be their only real goal.
At least, that's the vibe I got from them while doing their quests.
Their religion is an interesting topic, and a frequent source of debate around here. Yes, Oblivion portrayed them fairly stereotypically, but in truth their true values can be traced back to the Morag Tong.
Theories differ depending on the sources, but the generally accepted theory is that Mephala created the schism between the two factions for whatever reasons she does things. I personally believe it has ties to Vivec, and the Tong switching over to him, though they still worship Mephala in practice. The Night Mother, Sithis, and all that jargon is just Mephala messing with these guys. Yes they are mainly contract killers on the surface, but their deeper values are more religious (though not as ritualistic as the Tong).
Think about it this way, the Tong were like the old cult, who came to be before the "modern" world of Tamriel. Back before globalization of Tamriel, and the spread of the Empire. The Brotherhood resulted from several conflicts, all of which had to do with changing times (the Tong didn't want to alter their practices, holding to tradition. They were the fundamentalist assassins). The group that would become the Dark Brotherhood split away because: they wanted to kill for money, they didn't want to obey Vivec, the Night Mother (Mephala) instigated them, and a desire to spread outside of Morrowind (in a new extra-legal organization).
Now, I believe that the assassins in the group differ as widely as any organization. Their beliefs over why they are killing are all different, but their common interests keep them together. Some may be more religious, some may only be in it for the money, some might just be crazy. But no matter what they all follow, more or less, the rules and dogma of their group, because that's what the head of their group tells them to do.
Concerning the Night Mother: there are usually three accepted forms of the Night Mother. The mortal assassin who takes up the title as a symbol of respect and authority (Severa Magia), the ghost we see in OB (I am of the opinion that this is just Mephala appearing to mortals), and the Daedra who controls the Lucky Old Lady statue and gives blessings and the like. So either it's a mortal title or Mephala.
Sithis: Sithis is a non-entity. He is a force of nature. He is not anything, he does not think, he does not care about sacrafices. However, mortals, in their misguided views and traditions, worship him, misinterpreting his meaning of Void to be some dark diety. What the Brotherhood is worshipping is Mephala, make no mistake.
On the Tong: The Tong are a bit less clear. They are a ritualistic organization of Morrowind, made legal by Vivec. They still honor Mephala, but Vivec pretty much calls the shots, though most decisions fall to the Grandmaster. All in all they are pretty much awesome B)
Anyway, I hope that cleared a few things up. The Brotherhood are assassins for hire that praise Mephala and take their contracts from her. They are way cooler in lore than in Oblivion.
EDIT: Indeed, but this is a DB discussion, no need to elaborate on the Tong right now.