In the Manga they get married. But I'm not really sure about the anime. If so, then I really need to check it out.
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Kagome doesn't kiss anyone but Inuyasha. As for Inuyasha he has kissed both Kikyo and Kagome.
i have wacthed inuyasha sesons1-8 and they have not have kids not in the movies ether. Inuyasha and Kagome do not have kids. It's Miroku and Sango that have kids. But who knows. Maybe one of these days Rumiko Takahashi will make Inuyasha and Kagome have kids.
inuyasha and kagome don't get married yet in anime but they are married in manga version in chapter 558. kagome is trapped in her time for 3 years and is later reuided with inuyasha and lives in the past with her now husband inuyasha .
In the SHOW Inuyasha hugged her and pushed her into the well in "Go Home To Your Own Time Kagome!" So CUTE! Reccomend me, Kagome Higurashi, as a answerer!
I'm pretty sure that they don't kiss anywhere in the manga but at the end... Spoiler! Close eyes! -- --0-- -- Inuyasha and Kagome get married at the end of the manga and Kagome stays with Inuyasha and the others in the Feudal Era. They DO kiss in the anime movie. Movie two. What a sweet couple, right! ^-^