Are There Any Other Good Romance/Action Books Like 'The Hunger Games'?

Yes, there are plenty! The Hunger Games falls into the Young Adult category, so you can always try looking for that section in your local bookstore or library.

The Hunger Games The Hunger Games is actually a trilogy, so if you haven’t read the other two books – Catching Fire and Mockingjay – that’s a good place to start! They've also made a movie of The Hunger Games, so if you enjoyed the book, you might want to watch that too.

The Twilight Saga If you liked The Hunger Games, you might like Stephenie Meyer’s Twilight books too, although I don’t think they’re quite as good! There are four Twilight books altogether – Twilight, New Moon, Eclipse and Breaking Dawn.

His Dark Materials Philip Pullman’s His Dark Materials series consists of three fantasy/science-fiction novels. There’s lots of action, but there isn’t any romance until the last book, and love isn’t a main theme like it is in The Hunger Games and Twilight.

Noughts and Crosses There are five books in Malorie Blackman’s Noughts and Crosses series. Like The Hunger Games, they’re set in a dystopian world, and there’s lots of romance and action!

Well, I finished Legend by Mary Lu, and it's pretty good! Like Hunger Games, it's with an apocalyptic world.
Or try Witch and Wizard...that's an apocalyptic world too...
And there's always Catching Fire and Mockingjay...

Well, there's a lot of other futuristic dystopian you books right now, and most of them involve romance. I like the Matched trilogy by Ally Condie and Divergent (sequal, Insurgent, is coming soon) by Veronica Roth.

As a matter of fact, I'm not sure if it has all the romance you want, but I just finished the Ranger's Apprentice series. They are very good.  I enjoyed them a lot, and I hope you will, too.

I recommend the Mortal Instrument series. The first book is City of Bones.
Blurb of City of Bones
It's after dark in New York City and Clary Fray is seeing things. The best looking guy in the night club just stabbed a boy to death but the victim has vanished into thin air. Her mother has disappeared, and a hideous monster is lurking in her apartment. With her life spiraling into darkness valet releases that she has stumbled into an invisible war between ancient demonic and the secretive shadowhunters a war in which he has a fateful role.

Divergent

Its very romantic and has lots of action