The Office 2.0 conference was set up almost entirely without paper (except for some checks that paid for sponsorships). Even the contracts necessary to set up the show were signed electronically, using EchoSign. There are other companies that provide services to create legally binding signatures, such as DocuSign (review), but EchoSign has simplicity going for it.
If you want to have a document "signed" electronically, EchoSign will convert it to a PDF, send it to your designated recipient, and give you the option to have it signed via a Web form, or with a pen, via fax. For e-signatures, the service confirms when the recipient opened the document and when they "signed" it with keystrokes on their computer; this transaction is actually a legally valid signature. Still, traditionalists might want to use the fax option, in which case EchoSign sends your recipient a PDF of your file, which they then print, sign, and fax to the number printed on a special cover sheet. This fax is then routed to your EchoSign account automatically. Whichever method you use, EchoSign keeps track of all your contracts and can remind you of which ones are pending signature.
The product does not confirm that the person who signed the document is who you intend it to be. It's an electronic record-keeping and workflow service, not a notary. But electronic signatures are more legal than you probably think, and much easier to manage than paper transactions.
If you only need to manage the odd contract from time to time, you probably don't need this product, which is $12.95 a month. But if managing and tracking contracts takes up a noticeable portion of your work time, EchoSign could probably get some of it back for you. There's also a version that integrates with SalesForce.com, which is great for salespeople.