You might be surprised to learn that very little has changed in the world of business communications in the past 10 years even as the ways to communicate have proliferated. While handwritten letters have been reduced to a novelty item and printed or typed letters are used only for the most formal communications, email still rules the day.
For the record, a recent report by the Radicati Group estimated that there are 3.1 billion email accounts -- the greatest number of those are on Hotmail, Yahoo! Mail and GMail with an estimated 855 million split between the three services . Compare this number to Facebook's 800 million users and Twitter's 100 million users and remember that on both services, only half of all users are considered active or regular. The only real contender to email by the numbers is SMS (text messages) via mobile phones; about 3/4 of the world's 4 billion mobile phones are able to send and receive text messages and last year, over 6.1 trillion text messages were sent.
While it may be convenient to dash off a quick direct message in Twitter or private message in Facebook, it's important to remember that both are services that silo information; Facebook and Twitter work hard to make your information non-portable and transient at the same time (ever try to search your Facebook messages or scroll back through Twitter DMs?). Similarly, text messages are fluid and transient. Most of us do not back up or forward our text messages to an email client. However, it is worth noting that most teens and young adults prefer texting to other modes of communication.
Email, however, has proven itself to be a suitable replacement for written communications. It's easy to archive, easy to search and easy to share. That last factor, easy to share, is one of email's superior traits is that it is easy (sometimes too easy) to send a message to or have a conversation with multiple people. Before email, secretaries were kept busy with carbon paper or photocopiers making copies to send to all parties now just adding an email address to a CC field is all it takes. That it can be archived and searched gives it more permanence like the paper trail it has succeeded.
If you're communicating with friends or family, it doesn't really matter which platform you use but if you want to be taken seriously in business, use email.