Here are some books that I've read after the Twilight series and really enjoyed:
The Host by Stephenie Meyer -
Melanie Stryder refuses to fade away. The earth has been invaded by a species that take over the minds of their human hosts while leaving their bodies intact, and most of humanity has succumbed.
Wanderer, the invading "soul" who has been given Melanie's body, knew about the challenges of living inside a human: the overwhelming emotions, the too vivid memories. But there was one difficulty Wanderer didn't expect: the former tenant of her body refusing to relinquish possession of her mind.
Melanie fills Wanderer's thoughts with visions of the man Melanie loves-Jared, a human who still lives in hiding. Unable to separate herself from her body's desires, Wanderer yearns for a man she's never met. As outside forces make Wanderer and Melanie unwilling allies, they set off to search for the man they both love.
The Hunger Games by Suzanne Collins -
Katniss is a 16-year-old girl living with her mother and younger sister in the poorest district of Panem, the remains of what used be the United States. Long ago the districts waged war on the Capitol and were defeated. As part of the surrender terms, each district agreed to send one boy and one girl to appear in an annual televised event called, "The Hunger Games." The terrain, rules, and level of audience participation may change but one thing is constant: kill or be killed. When Kat's sister is chosen by lottery, Kat steps up to go in her place.
Velocity by Dean Koontz -
Bill Wile is an easygoing, hardworking guy who leads a quiet, ordinary life. But that is about to change. One evening, after his usual eight-hour bartending shift, he finds a typewritten note under the windshield wiper of his car. "If you don't take this note to the police and get them involved, I will kill a lovely blond schoolteacher. If you do take this note to the police, I will instead kill an elderly woman active in charity work. You have four hours to decide. The choice is yours."
The Mortal Instruments series by Cassandra Clare -
(City of Bones, City of Ashes, City of Glass)
I'm reading these right now, and they're absolutely amazing! I d don't want to put the summary they have online, because it might give something away. But they're awesome, so read them! Haha.