Paper: Just as good as a pencil and notebook

Paper, free
There are no shortage of writing and painting apps on the iPad, but FiftyThree's Paper is the one to get first. This app enables you to sketch, and draw, with a variety of different pens, pencils and brushes, and the scissors act like cut-and-paste but for your scribbles. There's also a neat Pen and Ruler tool that you can use to draw arrows, squares, triangles and other shapes (it makes for an effective flowchart too).
When it comes to picking the best apps for iPad, we chose Paper hands-down to be number one in our list. No other app recreates the experience of working with a physical medium quite as well. Like its name suggests, its paper for your iPad.