I took a look at Daniel Shiffman's article about Emails in Processing and a tried to make a simplified version of it. With this code you can receive emails with pop3 from  Hotmail and Gmail and sent emails with smtp in Gmail. Unfortunately you can't do both in one sketch and you have to include pop3.jar in the sketch althouch it is included in the Java Mail API.
Receive emails (example):

1. PMailReceiver receiver;
2. 
   
3. public void setup() {
4. size(500, 500);
5. receiver=new PMailReceiver(this,"pop.gmail.com", "YOURUSERNAME@gmail.com", "YOURPASSWORD");
6. receiver.update();
   
7. 
   
8. println(receiver.getMessageCount() + " total messages.");
   
9. PMessage[] messages=receiver.getUnreadMessages();
   
10.  for (int i=0;i<messages.length;i++) {
11.     println("---------------------");
12.     println("Message # " + (i+1));
13.     println("From: " + messages[i].getFrom());
14.     println("Subject: " + messages[i].getSubject());
15.     println("Message:");
16.     println(messages[i].getMessage());
17.   }
18.   receiver.quit();
19. }
    

Sending emails (example):

1. PMailSender sender;
2. 
   
3. public void setup() {
     size(500, 500);
4. sender=new PMailSender(this,"smtp.gmail.com", "YOURUSERNAME@gmail.com", "YOURPASSWORD");
   
5. sender.setFrom("NAME@...", "NAME");
   
6. sender.setTo("NAME@...");
   
7. sender.update();
   
8. sender.send("Hello World", "test");
   
9. println("Email sent!");   
10. }