Except without the time travel elements.

Basically the female lead and others have/want to save the male lead from something. The male and female lead are in love with each other. They save him and then the leads end up together.

Will take any kind of genre as long as there's romance.

Kanata Kara is the first one I can think up... The saving doesn't come until later, but yeah. Let me come back after looking through my list when I'm freer. Lol... If I remember that is.