Art Flow
Art Flow is a great tool for both amateurs and professionals. There is a free version with limited features, and a pro version as well. It allows working on layers (upto 7-16), and also export to PSD (for the photoshop fellas). Infinite undo and redo is possible. The free version has 20 basic tools, 2 layers, limited undo options (upto 6 times), and no PSD export.
Sketchbook Express
Autodesk Sketchbook Express is the free version of Sketchbook Pro. It is a professional paint application for all android phones with screen size 4" and above. Upto 3 layers are allowed. The pro version has more features and layer options. Size: 11.43 MB
Infinite Painter
Infinite Painter boasts of 80+ natura brushes, you create new brushes and change brush settings, layers and photoshop blend modes, and a plethora of other features. There are in-app purchases as well. Size: 17.4 MB
Sketch Master
Sketch Master gives you unlimited layers, 7 brushes, import and share images, toggle visibility and adjust layer opacity. his app is completely free. Size: 2.82 MB
Painter Mobile
Painter Mobile gives you upto 15 layers. This app is optimized for Wacom Cintiq Companion Hybrid and stylus devices. You can also map functions to hardware keys and gestures. In-app purchases. Size: 15.63 MB
Layer Paint
Layer Paint is a completely free app. It is only for smartphones, or vertical retention devices. PSD format import and export enabled. Size: 3.26 MB
MediBang Paint
MediBang Paint is good for comics and manga artists. A unique feature is the speech-to-text feature for writing the dialogues. You get 60 free brushes, layer support, and a lot of cool features. Completely free. Size: 7.51 MB
If there are apps which you feel should be on this list, mention them in the comments, we will add them to the list! If you are a newbie and want to learn how to create android apps, refer this book : Android Programming: The Big Nerd Ranch Guide, this is the most popular book among android developers.