Main Goal: Although some members joined Akatsuki to further their own goals, all are united in Akatsuki's ultimate goal of gaining domination over the Shinobi world. The leader, Pain, has created a three-step process to work their way towards this goal. First, they plan to obtain a large amount of money to support their organization. Second, they plan to set up a mercenary group loyal only to Akatsuki. To build their reputation, they plan to accept any mission below the usual cost and operate off of the excess funds earned in the first part of their plan. Because there haven't been any wars in some time, the established shinobi villages can't afford to charge such low prices, leading the smaller countries to hire Akatsuki over the more expensive shinobi villages. By using the tailed beasts, Akatsuki can start wars and then immediately quell them, solidifying their reputation and convincing every country to depend on them, thus cornering the market in shinobi labor. Without any business, the other shinobi villages will collapse due to a lack of funds. Finally, after Akatsuki is the only major force of shinobi in existence, they can easily conquer the other countries. Members do not automatically learn of the plan upon joining; Hidan did not find out about it until he had been a member for quite some time.
The tailed beasts, nine gigantic demons of immense power, are the focus of much of Akatsuki's effort and screentime within the series. Each Akatsuki member is assigned to capture one of the nine beasts alive or, in most cases, the person that beast has been sealed into. Akatsuki has so far obtained seven of the nine: the first through the seventh tailed beasts.
However, this plan may just be a ruse as Akatsuki's three most prominent members have two separate goals in mind instead of controlling the world; one of which involves world peace.
Pain's Goal: Pain later went into further detail on the tailed beasts' role in his plans. The beasts would be used to create a deadly kinjutsu technique that could wipe out one of the five great nations in an instant, so if countries go to war and do not have ninja villages to fight for them they would turn to the Akatsuki and their technique. Whichever side uses the technique first would wipe out the opposing country, which would scare them into never using their weapon again, and scare the other countries to never start a war or they would be wiped out too. Through the mutual fear, war would cease to exist, and the world would know everlasting peace.
This greatly conflicts with Madara's plan so this goal could in fact be a secret goal that only Pain and Konan are aware of.
Madara's Goal: Madara Uchiha, Akatsuki's benefactor, has another goal in mind instead of world domination. Madara wishes to use the beasts to return his Sharingan to its true power. Anything after this point is currently unknown but he has shown interest in destroying Konoha.
Itachi's Goal: Itachi Uchiha's Goal was to act as a spy for Konoha, so he could alert them in case of danger. After he died from a serious disease, there appears to be no more informant within Akatsuki. It is believed that he was Jiraiya's unknown informant, indirectly dropping information to him through others.
Sasuke's Goal: Sasuke Uchiha's Goal is to use Akatsuki so he can get revenge on Konoha for having persecuted the Uchiha and forcing Itachi to kill his clan. Madara offers him the eight-tailed beast if he succeeds in capturing it, but while Sasuke succeeds in doing so, he appears confident that his Mangekyo Sharingan is enough to destroy the Leaf Village