Send e-mail in Android using the JavaMail API using Gmail authentication.
Steps to create a sample Project:
MailSenderActivity.java:
public class MailSenderActivity extends Activity {
    
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
        
        final Button send = (Button) this.findViewById(R.id.send);
        send.setOnClickListener(new View.OnClickListener() {
            
            public void onClick(View v) {
                try {   
                    GMailSender sender = new GMailSender("username@gmail.com", "password");
                    sender.sendMail("This is Subject",   
                            "This is Body",   
                            "user@gmail.com",   
                            "user@yahoo.com");   
                } catch (Exception e) {   
                    Log.e("SendMail", e.getMessage(), e);   
                } 
                
            }
        });
        
    }
}
GMailSender.java:
public class GMailSender extends javax.mail.Authenticator {   
    private String mailhost = "smtp.gmail.com";   
    private String user;   
    private String password;   
    private Session session;   
  
    static {   
        Security.addProvider(new com.provider.JSSEProvider());   
    }  
  
    public GMailSender(String user, String password) {   
        this.user = user;   
        this.password = password;   
  
        Properties props = new Properties();   
        props.setProperty("mail.transport.protocol", "smtp");   
        props.setProperty("mail.host", mailhost);   
        props.put("mail.smtp.auth", "true");   
        props.put("mail.smtp.port", "465");   
        props.put("mail.smtp.socketFactory.port", "465");   
        props.put("mail.smtp.socketFactory.class",   
                "javax.net.ssl.SSLSocketFactory");   
        props.put("mail.smtp.socketFactory.fallback", "false");   
        props.setProperty("mail.smtp.quitwait", "false");   
  
        session = Session.getDefaultInstance(props, this);   
    }   
  
    protected PasswordAuthentication getPasswordAuthentication() {   
        return new PasswordAuthentication(user, password);   
    }   
  
    public synchronized void sendMail(String subject, String body, String sender, String recipients) throws Exception {   
        try{
        MimeMessage message = new MimeMessage(session);   
        DataHandler handler = new DataHandler(new ByteArrayDataSource(body.getBytes(), "text/plain"));   
        message.setSender(new InternetAddress(sender));   
        message.setSubject(subject);   
        message.setDataHandler(handler);   
        if (recipients.indexOf(',') > 0)   
            message.setRecipients(Message.RecipientType.TO, InternetAddress.parse(recipients));   
        else  
            message.setRecipient(Message.RecipientType.TO, new InternetAddress(recipients));   
        Transport.send(message);   
        }catch(Exception e){
            
        }
    }   
  
    public class ByteArrayDataSource implements DataSource {   
        private byte[] data;   
        private String type;   
  
        public ByteArrayDataSource(byte[] data, String type) {   
            super();   
            this.data = data;   
            this.type = type;   
        }   
  
        public ByteArrayDataSource(byte[] data) {   
            super();   
            this.data = data;   
        }   
  
        public void setType(String type) {   
            this.type = type;   
        }   
  
        public String getContentType() {   
            if (type == null)   
                return "application/octet-stream";   
            else  
                return type;   
        }   
  
        public InputStream getInputStream() throws IOException {   
            return new ByteArrayInputStream(data);   
        }   
  
        public String getName() {   
            return "ByteArrayDataSource";   
        }   
  
        public OutputStream getOutputStream() throws IOException {   
            throw new IOException("Not Supported");   
        }   
    }   
}  
JSSEProvider.java:
/*
 *  Licensed to the Apache Software Foundation (ASF) under one or more
 *  contributor license agreements.  See the NOTICE file distributed with
 *  this work for additional information regarding copyright ownership.
 *  The ASF licenses this file to You under the Apache License, Version 2.0
 *  (the "License"); you may not use this file except in compliance with
 *  the License.  You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */
/**
 * @author Alexander Y. Kleymenov
 * @version $Revision$
 */
import java.security.AccessController;
import java.security.Provider;
public final class JSSEProvider extends Provider {
    public JSSEProvider() {
        super("HarmonyJSSE", 1.0, "Harmony JSSE Provider");
        AccessController.doPrivileged(new java.security.PrivilegedAction<Void>() {
            public Void run() {
                put("SSLContext.TLS",
                        "org.apache.harmony.xnet.provider.jsse.SSLContextImpl");
                put("Alg.Alias.SSLContext.TLSv1", "TLS");
                put("KeyManagerFactory.X509",
                        "org.apache.harmony.xnet.provider.jsse.KeyManagerFactoryImpl");
                put("TrustManagerFactory.X509",
                        "org.apache.harmony.xnet.provider.jsse.TrustManagerFactoryImpl");
                return null;
            }
        });
    }
}
Add the following three jars to your Android Project.
Check this post if you don't know how.
And don't forget to add the following line in your manifest:
<uses-permission android:name="android.permission.INTERNET" />
Adjust your account access settings for less secure apps by visiting this link:
https://www.google.com/settings/security/lesssecureapps.
UPD 2023: Less Secure Apps has been deprecated. To access your account, you will need to enable Two Factor Authentication and use App Password with the settings provided in the image below:

Run the project and check your recipient mail account for the mail.
P.S.: Please keep in mind that performing network operations directly from an Activity in Android is not allowed. Hence, it is highly recommended to use AsyncTask or IntentService to avoid encountering a network on main thread exception.
Jar files: https://code.google.com/archive/p/javamail-android/