One of my birds is so fidgety but he comes to me when he's in the mood. And he always nibbles my hand - its adorable.
My other bird loves playing by biting me - she's like her mom. She plays aggressively, and she's so playful.

And she flies to my hand when I say, "Heidi come." But now she's nesting and has been spending most of her time just sitting in the nest box.

And my other parakeet acts like a finch - he's so leight, and he practically has a heart attack when I put my hand by him. He occasionally comes, but flies away a few seconds later.
And my other parakeet is 10 years old and doesn't do much anymore...