These were one of the first YA dystopian series I read. I fell in love with the plight of the characters and the energy and tension of the story. While the second two books were also good, as a stand along, the first is my favorite. I assume most readers will know of these already so I won't recap their plots.
Divergent / Insurgent / #3 - Veronica Roth
Set in Chicago, the world is divided into five factions, each focused on a particular virture. At the age of 16, each citizen must chose their faction, one with they will stay with the rest of their lives. Our female protagonist must decide to stay with her family, or go with her gut. And of course this all leads to running, fighting, a little falling in love... the typical YA dystopian plot.
Legend / Prodigy / Champion (coming soon) - Marie Lu
In a divided United States an elite member of society, June, must partner with the country's most wanted criminal to discover what's really going on in the government and try to reconcile the nation. I think this would make a great movie, would be similar to many military fantasy movies and lots of good action.
Delirium / Pandemonium / Requiem - Lauren Oliver
Love is a desease. Everyone gets a cure on their 18th birthday. But between then and now, dun, dun, dun.... This series has a really strong second book and I'm really looking forward to reading the last book in the series. (I just discovered there are also short ebooks between each of the main 3 books, more to enjoy)
Honorary Mentions...
The Mortal Instrument Series: City of Bones / City of Ashes / City of Glass / City of Fallen Angels / City of Lost Souls / City of Heavenly Fire - Cassandra Clare
The Infernal Devices Series: Clockwork Angel / Clockwork Prince / Clockwork Princess - Cassandra Clare
The Uglies: Uglies / Pretties / Specials / Extras - Scott Westerfeld