It's pretty obvious that an easy way to get rid of paper is to get rid of printed books. Instead of lugging around textbooks, research materials, and airplane fodder, download the Amazon Kindle app. Sure, your tablet may not be an easy-on-the eyes e-Ink e-reader, but it's easy enough for quick business reading on a cross-country flight. The Kindle app lets you access Kindle books (including library books), and has several nice features including different backgrounds, a built-in dictionary, and adjustable text size.
Keeping track of business cards is almost impossible without a Rolodex--and really, who's got a Rolodex these days? CamCard is like a virtual Rolodex on your tablet. This app, available for iOS and Android (there's even an iPad-specific HD version), is an advanced business card reader. Just snap a photo of a business card, and the app extracts relevant details, such as company name, job title, and phone number, then adds them to your contact list. CamCard is fairly effective at reading cards and converting text, but you can also edit fields and add notes manually. (If you're on a Windows 8 tablet, we couldn't find an excellent, similar app, so stash your business cards in Evernote.)
Adobe's e-signature app lets you sign documents, send documents for signatures, get documents signed in person, or sign documents for other EchoSign users. Upload documents from your SkyDrive, Dropbox, Google Drive, or Box account. You can also upload photos from your tablet (for example, if you happened to take a photo of the document that needs to be signed). The first five contracts you sign per month on EchoSign are free. After that, you'll need a subscription (between $14.95/month and $399/month).