With everyone jumping on the Twitter train, naturally Evernote was going to as well. So now with the Evernote-Twitter integration, you can send yourself notes from Twitter. If you already have an Evernote account, just follow myEN from your Twitter profile (myEN will follow you back), then after you receive a direct message back with a confirmation link, you can connect your Twitter and Evernote accounts.
To send a private, direct message, send a direct message to myEN which will go to your Evernote account. And for public notes, just add @myEN in a tweet to have Evernote include it.