Adobe Ideas is a free basic sketching program for iOS from the developers behind the hugely popular and standard-setting Adobe Creative Suite.
This simple drawing application lets you sketch, save, and share (via e-mailed PDF) "ideas," drawings that you create with the app's adjustable brush tool on a blank canvas that lets you pan and zoom in and out. The app's hideable touch toolbar gives you a brush, eraser, hand tool (for panning), undo (up to 50 times), and settings to change the size, color, and opacity of the brush. You can also import photos, which can give you an easy way to trace a photo or mark up a picture or document. The app only supports two layers (one for a photo and one for drawing), but you can buy support for up to 10 as an in-app purchase. You can also use imported photos to create complementary color palettes, from your own photos or anything in your camera roll, such as screen captures from your browser. This is similar to Adobe's Kuler Web site, just as many of Adobe Ideas' features will feel familiar to users of Illustrator and other Adobe apps. (For example, the brush tool immediately "smooths" your lines into vector drawings as soon as you lift your finger.)
Adobe Ideas may not be a high-powered drawing app (and it could do a better job of explaining its own features), but it gives you a lot of functionality for free, all in a clean, unobtrusive, and even kid-friendly interface.