At the beginning of the series, there seems to be a continuity error in that Naraku, disguised as Inuyasha, steals the Shikon Jewel but later, the real Inuyasha is shown to have stolen it when he is sealed to the tree by Kikyo's arrow.
Actually what happens here is explained in bits and pieces later in the series. Naraku desires to taint the Shikon Jewel by turning Kikyo and Inuyasha against one another. To do this, he takes the form of Inuyasha, steals the jewel and attacks Kikyo. Naraku then replaced the jewel, transformed into Kikyo and attacked Inuyasha, provoking him to steal the Jewel. This betrayal taints the Shikon Jewel, which makes it more valuable to Naraku. Naraku didn't plan on Kikyo taking the jewel with her in death though. Submitted by zach