Spoilers
!! Please note that this section is current as of chapter 312, at the introduction of Hidan and Kakuzu.
SPOILERS up to chapter 238/episode 135 (before the timeskip)
Before the timeskip, the members gather together for the first time since Orochimaru left the group and finally reveal a few plans. First, they intend to kill Orochimaru. But they only have 3 years left, so they must all complete their missions by then. The leader also adds that as long as they have the kyuubi, they can have everything.
Their headquarters seems to be in a dark, isolated cave in River Country. When the members meet, they are not physically present, but rather, are present with a projected image of themselves. It gives off this white static effect, which only adds to their badass image.
SPOILERS after chapter 247+ (after the timeskip)
After the timeskip, Akatsuki begins to take action.
We are introduced to a couple more members, Sasori and Deidara, who are seeking the jinchuuriki, the power of human sacrifice (in this case, the monster sealed within a human). This reveals that Akatsuki are after the nine bijuus, including Gaara's ichibi and Naruto's kyuubi. They want to have that power for their own control, so each member sets out to capture their own jinchuuriki. "One person per beast," as Sasori puts it (ch 264). Their ultimate goal is yet to be uncovered.
Chiyo-baasan explained that Akatsuki had to wait three years to come after Naruto again, not only because he was under the care of Jiraiya, thus making him untouchable in those years, but it takes time to prepare for the process of extracting the bijuu from the host body.
SPOILERS as of chapter 312
After Sasuke's reintroduction in the manga, Akatsuki begins moving again.
We are introduced to two more members, Hidan and Kakuzu, who are currently pursuing the last jinchuuriki, the female nibi (two tails). Kakuzu comments that she is the last one, so it is suggested that the Akatsuki have gotten all their jinchuuriki targets, besides Naruto's kyuubi. Hidan also acknowledges that he is the least skilled member of Akatsuki, as he is jinchuuriki-less.
Orochimaru, Kabuto, and Sasuke are aware of what the Akatsuki are up to, and know that the members will get in the way of Sasuke's revenge. So they are leaving it up to Naruto-tachi to take care of the Akatsuki members.