If you are a professional artist, Sketchbook is a must-have app for you. Developed by Autodesk, this free app provides a set of dedicated sketching tools for devices with screen sizes 7" or smaller. Whether you prefer to capture your ideas on a paper napkin or draw beautiful sketches of people that you see everyday, this application lets you take your creativity to a level that you want. Though the app is for professionals, it can be used by pretty much anyone who has a flair for drawing and sketching.
While not strictly a sketching or a doodling app, it is a useful addition to the list, nonetheless. Evernote's Skitch lets you annotate images and even PDF files so that you can be more expressive with the data you already have. It's a great tool to snap a picture of something, mark it up with your own ideas, and then send it to someone who can help transform the idea to reality. It is definitely worth a try for the creative types.
Doodle Magic is an app that kids will love. It is simple, without any extra bells and whistles, and just works. You get to draw on a black background with bright glowing colors, which might seem a bit odd at first, but results in some great artwork if you are good at it.
If you are someone who likes to have more fun with your photos, Doodle Text is an app for you. Once installed, you'll be able to doodle on your photos, add some funky effects, and then send the picture to your friends. This means that you can draw a moustache, make yourself look like a ninja, or even type in messages for your loved ones. As far as sharing features go, this app has plenty with even an ability to post to your Facebook wall. Go ahead; share your masterpieces with your buddies!
Bamboo Paper is an app with a simple goal: Turn your Android smartphone into paper. Among the apps mentioned in this list, this one is probably the most accurate and the most useful one. With precise inking tools, annotation capabilities, and much more, Bamboo Paper really strikes out as a doodling app that you can actually use in your daily life. Once installed, you can create your own notebooks wherein you can sketch, write, or doodle anything you want. Once you are done, you can share those notebooks with colleagues and friends via Dropbox, Evernote, Twitter, and Tumblr.
Infinite Painter is an app specially designed for Galaxy Note smartphones that come with S-pen or similar styluses. Once installed, there is a lot you can do with this app. Aimed for creative minds, this app is perfect if you are someone who paints a lot or likes sketching. Instead of frantically searching for a canvas every time you head out, you can have a full-fledged virtual canvas at your disposal. Though using the app on smaller (5 inch or less) devices won't do it much justice, it is still a good investment if you are serious about sketching.