Originally Answered: Good book series besides twilight or harry potter?
Well, if you like Sci Fi (which is what Hunger Games is), you could try Scott Westerfeld. He has several series, including the acclaimed Uglies series. Like Hunger Games, it takes place in the distant future after humanity has messed itself up. Only in this case, it has rebuilt to a new society, where there is no conflict or war. On your 16th birthday, you undergo a surgery to make you beautiful and perfect. Tally, the protagonist, is excited to undergo her surgery. But when her friend, Shay, runs away before her birthday, Tally is given a choice: to track down Shay, or be refused the surgery and stay ugly forever. Through her travels, she learns some unsettling truths about her world, finding out that things might not be as pretty as they seem. There are 4 books in the series, and Westerfeld has several other awesome books to check out.
Other sci fi series:
Incarceron by Catherine Fisher
Matched by Allie Condie (Less action and more drama.... kind of Twilight meets Hunger Games, but with less whining)
The Forest of Hands and Teeth by Carrie Ryan (depressing... but zombies. Zombies are pretty much always good)
The Giver series by Lois Lowry (also depressing, but so, so good. More concentrated on human emotions then action, and there isn't much romance.)
If you want to go for more fantasy stuff (Harry Potter), then you could try:
Inkheart by Cornelia Funke (a man with the power to read characters out of books... first book is good, numbers 2 &3 are epic.)
Chronicles of Chrestomanci by Diana Wynne Jones (everything written by her is awesome, but this is her longest series, and is also compared to HP a lot)
Tithe by Holly Black (little bit more mature... there's some language, and some adult situations, so keep this one on the shelf for a little while if you're on the young side of things... her new series is also very good).
Anything ever written by Kelley Armstrong (she's pretty fantastic... she has two series for teens, and a really long series for adults. If you're younger, stick with the teens, because the adult series does get graphic in terms of sex/violence)
Somebody already mentioned Percy Jackson, and I'll second that... but no comparisons to Harry Potter. They are actually quite different, though both very good!
If you're an older type person, or have a very advanced reading level, I would advise you check out Jasper Fforde. His new sci-fi series, Shades of Grey, is super awesome. But he is an adult level writer.
Hopefully you'll find at least one good series on here... I tried to give you a wide variety, though I tried to stay away from the super love triangle-y Twilight-esque stuff. Good luck!