Inuyasha & kagome would have to be the big couple in the story. At first they hated each others guts, now as they travel  together & inuyasha gets feelings for kagome & so does  kagome (hint kagome kisses him in the second movie). But Inuyasha seems to have feelings for kagome still & kagome gets jealous.

Sango & Miroku

Sango & miroku. At first they were only companions & miroku would flirt with every woman he met, which made sango jealous. In ep. 132 miroku proposes to sango & she says yes & asks if he won't cheat on her. But miroku says nothing. hes gonna cheat on her.