View value of password edittext while a button is pressed

 yourButton.setOnTouchListener(new OnTouchListener() {
        public boolean onTouch(View v, MotionEvent event) {

               switch ( event.getAction() ) {
                case MotionEvent.ACTION_DOWN: 
                   editText.setInputType(InputType.TYPE_CLASS_TEXT);
                break;
                case MotionEvent.ACTION_UP: 
                    editText.setInputType(InputType.TYPE_CLASS_TEXT | InputType.TYPE_TEXT_VARIATION_PASSWORD);
                break;
                }
                return true;
        }
    });

I found one of best solution for Design Support Library Users:

It is really easy to achieve with the newest Support Library v24.2.0.

What you need to do is just:

1. Add the design library to your dependencies

   dependencies {
        compile "com.android.support:design:24.2.0"
   }
   

2. Use TextInputEditText in conjunction with TextInputLayout

   <android.support.design.widget.TextInputLayout
       android:id="@+id/etPasswordLayout"
       android:layout_width="match_parent"
       android:layout_height="wrap_content"
       app:passwordToggleEnabled="true"
       android:layout_marginBottom="@dimen/login_spacing_bottom">
   
       <android.support.design.widget.TextInputEditText
           android:id="@+id/etPassword"
           android:layout_width="match_parent"
           android:layout_height="wrap_content"
           android:hint="@string/fragment_login_password_hint"
           android:inputType="textPassword"/>
   </android.support.design.widget.TextInputLayout>
   

The passwordToggleEnabled attribute will do the job!

3. In your root layout don't forget to add xmlns:app="http://schemas.android.com/apk/res-auto"

4. You can customize your password toggle by using:

app:passwordToggleDrawable - Drawable to use as the password input visibility toggle icon.
app:passwordToggleTint - Icon to use for the password input visibility toggle.
app:passwordToggleTintMode - Blending mode used to apply the background tint.

More details in TextInputLayout documentation.