Cook beans in large pot of boiling salted water until crisp-tender, about 5 minutes. Drain. Place beans in bowl of ice water to cool. Drain well. Pat dry with paper towels. (Can be made 1 day ahead. Wrap in paper towels and refrigerate.)
Heat oil in heavy large skillet over medium-low heat. Add pine nuts and sauté until light brown, about 6 minutes. Add garlic; stir 1 minute. Add green beans to skillet; sauté until heated through, about 5 minutes. Stir in basil. Season with salt and pepper. Transfer to bowl and serve.