It's a matter of personal opinion, but in the last episode (Episode 26: Toward Tomorrow) of Inuyasha: Kanketsuhen(Inuyasha: The Final Act in English), Koga is shown to have married Ayame, while Kagome and Inuyasha marry. They all stay in the Feudal Era.
You can watch this episode and the others in The Final Act at Shonen Sunday's anime website.
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ayame is a wolf deamon that koga promised to marry when he saved her in the past
Naraku takes out most of his clan, and eventually Koga loses his two shards of the Shikon Jewel and he returns to the remnants of his wolf pack. As to his thing for Kagome, he lets up on his affection and devotion to her, and tells Kagome that if she ever gets tired of Inuyasha, he is still available. But in the end, he marries Ayame.
古賀 Pronunciation: Koga
It was the episode where koga fell in love with kagome and him and inuyasha battled him for the first time
Teuchi and his daughter Ayame http://naruto.wikia.com/wiki/Teuchi http://naruto.wikia.com/wiki/Ayame