'The Elemental Series' by Elizabeth Hunter was very good. Similar to 'Twilight', its about a young girl meeting a vampire and falling in love, and the ups and downs they face as a human and vampire couple, but its also very different in a lot of ways. There are four books in the series, the first book is free on Kindle, last I looked, and the others are not expensive(under $5 a piece).
'Divergent' by Veronica Roth is very good, as well. This book has similarities to The Hunger Games, post apocalyptic with the world divided into groups, yet its still very different.
'Insurgent' is book two, also very good. The 3rd book won't be out until next Fall, and has yet to be named, BUT I am willing to wait because the first two are very good!
Hope that helped, can't wait to see what others post!