Evernote is a free* note-taking application that can be used via the Web or using a client for computer or mobile devices. You can use it to type notes, capture audio notes, and upload documents to your account; the company allows other software developers to work with it and as a result has many other software packages that will sync notes and documents with Evernote.
* the basic account is free, but there's a traffic limit. If you do a lot of syncing of large audio and video files to your Evernote account, you may be encouraged to upgrade to a paid plan. See this page for more info about Evernote.
As part of the Office suite of tools, OneNote has a native Windows client, but also allows you to work online via a Live.com/Outlook.com account. If you have an iPad, iPhone, iPod touch, or Android device, there's also a free app that syncs with Microsoft's servers, allowing you access to your OneNote notebooks.
Springpad is similar to Evernote in many respects. There's a Web-based client and apps for Apple's iOS-based devices and Android. Notes sync to the cloud, and you can store typed notes, audio and video files, and more. You can also make your notebooks public, if you feel like sharing.
Handwriting apps can be a fast way to take notes, especially if you find typing on a tablet keyboard difficult. You may, however, find it's easier writing with a touch-sensitive stylus, which adds another cost to the price of the tablet and app.
A handwriting app for the iPad, Noteshelf allows you to choose virtual paper designs appropriate to the kind of notes you'll be taking. You can also customize the covers of the books and save pages to your Evernote account.
Penultimate is developed by Evernote, and is a perennial favorite handwriting app for the iPad due to its functionality and low cost.