Android 4.0 supports Drag and Drop of Views. You register a listener on the View and you define other Views as possible drop targets, e.g. drop zones. To use this you register a listener on the View, e.g. a OnTouchListener or a LongClickListener. In this method you construct an object of type ClipData. This object can be used to contain data which can be passed to the Views which are defined a drop zones. The DragShadowBuilder allow you specify the look of the dragging operation. Typically you pass in the View directly, which will be shown for the drag operation.

// Assign the touch listener to your view which you want to move
findViewById(R.id.myimage1).setOnTouchListener(new MyTouchListener());

// This defines your touch listener
private final class MyTouchListener implements OnTouchListener {
  public boolean onTouch(View view, MotionEvent motionEvent) {
    if (motionEvent.getAction() == MotionEvent.ACTION_DOWN) {
      ClipData data = ClipData.newPlainText("", "");
      DragShadowBuilder shadowBuilder = new View.DragShadowBuilder(view);
      view.startDrag(data, shadowBuilder, view, 0);
      view.setVisibility(View.INVISIBLE);
      return true;
    } else {
    return false;
    }
  }
} 
A View which can be used as drag zone, gets a OnDragListener assigned via the setOnDragListener() method. In this  OnDragListener you can evaluate the events and react accordingly.
findViewById(R.id.bottomright).setOnDragListener(new MyDragListener());

class MyDragListener implements OnDragListener {
  Drawable enterShape = getResources().getDrawable(R.drawable.shape_droptarget);
  Drawable normalShape = getResources().getDrawable(R.drawable.shape);

  @Override
  public boolean onDrag(View v, DragEvent event) {
    int action = event.getAction();
    switch (event.getAction()) {
    case DragEvent.ACTION_DRAG_STARTED:
    // Do nothing
      break;
    case DragEvent.ACTION_DRAG_ENTERED:
      v.setBackgroundDrawable(enterShape);
      break;
    case DragEvent.ACTION_DRAG_EXITED:        
      v.setBackgroundDrawable(normalShape);
      break;
    case DragEvent.ACTION_DROP:
      // Dropped, reassign View to ViewGroup
      View view = (View) event.getLocalState();
      ViewGroup owner = (ViewGroup) view.getParent();
      owner.removeView(view);
      LinearLayout container = (LinearLayout) v;
      container.addView(view);
      view.setVisibility(View.VISIBLE);
      break;
    case DragEvent.ACTION_DRAG_ENDED:
      v.setBackgroundDrawable(normalShape);
      default:
      break;
    }
    return true;
  }
}

Create a new Android project called "de.vogella.android.draganddrop" with an Activity calledDragActivity. Create the "drawable" folder in your "res" directory. Create the "shape.xml" file in this folder.

<?xml version="1.0" encoding="UTF-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle" >

    <  stroke
        android:width="2dp"
        android:color="#FFFFFFFF" />

    <gradient
        android:angle="225"
        android:endColor="#DD2ECCFA"
        android:startColor="#DD000000" />

    <corners
        android:bottomLeftRadius="7dp"
        android:bottomRightRadius="7dp"
        android:topLeftRadius="7dp"
        android:topRightRadius="7dp" />

</shape> 
Create the "shape_droptarget.xml" file in the "drawable" folder.
<?xml version="1.0" encoding="UTF-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle" >

    <stroke
        android:width="2dp"
        android:color="#FFFF0000" />

    <gradient
        android:angle="225"
        android:endColor="#DD2ECCFA"
        android:startColor="#DD000000" />

    <corners
        android:bottomLeftRadius="7dp"
        android:bottomRightRadius="7dp"
        android:topLeftRadius="7dp"
        android:topRightRadius="7dp" />

</shape> 
Change the "res/layout/main.xml" to the following.
<?xml version="1.0" encoding="utf-8"?>
<GridLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:columnCount="2"
    android:columnWidth="300dp"
    android:orientation="vertical"
    android:rowCount="2"
    android:stretchMode="columnWidth" >

    <LinearLayout
        android:id="@+id/topleft"
        android:layout_width="160dp"
        android:layout_height="200dp"
        android:layout_column="0"
        android:layout_row="0"
        android:background="@drawable/shape" >

        <ImageView
            android:id="@+id/myimage1"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_column="0"
            android:layout_row="0"
            android:src="@drawable/ic_launcher" />
    </LinearLayout>

    <LinearLayout
        android:id="@+id/topright"
        android:layout_width="160dp"
        android:layout_height="200dp"
        android:layout_column="1"
        android:layout_row="0"
        android:background="@drawable/shape" >

        <ImageView
            android:id="@+id/myimage2"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_column="0"
            android:layout_row="0"
            android:src="@drawable/ic_launcher" />
    </LinearLayout>

    <LinearLayout
        android:id="@+id/bottomleft"
        android:layout_width="160dp"
        android:layout_height="200dp"
        android:layout_column="0"
        android:layout_row="1"
        android:background="@drawable/shape" >

        <ImageView
            android:id="@+id/myimage3"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:src="@drawable/ic_launcher" />
    </LinearLayout>

    <LinearLayout
        android:id="@+id/bottomright"
        android:layout_width="160dp"
        android:layout_height="200dp"
        android:layout_column="1"
        android:layout_row="1"
        android:background="@drawable/shape" >

        <ImageView
            android:id="@+id/myimage4"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_column="0"
            android:layout_row="0"
            android:src="@drawable/ic_launcher" />
    </LinearLayout>

</GridLayout> 
Change your Activity to the following.
package de.vogella.android.draganddrop;

import android.app.Activity;
import android.content.ClipData;
import android.graphics.drawable.Drawable;
import android.os.Bundle;
import android.view.DragEvent;
import android.view.MotionEvent;
import android.view.View;
import android.view.View.DragShadowBuilder;
import android.view.View.OnDragListener;
import android.view.View.OnTouchListener;
import android.view.ViewGroup;  
import android.widget.LinearLayout;

public class DragActivity extends Activity {

  @Override
  public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.main);
    findViewById(R.id.myimage1).setOnTouchListener(new MyTouchListener());
    findViewById(R.id.myimage2).setOnTouchListener(new MyTouchListener());
    findViewById(R.id.myimage3).setOnTouchListener(new MyTouchListener());
    findViewById(R.id.myimage4).setOnTouchListener(new MyTouchListener());
    findViewById(R.id.topleft).setOnDragListener(new MyDragListener());
    findViewById(R.id.topright).setOnDragListener(new MyDragListener());
    findViewById(R.id.bottomleft).setOnDragListener(new MyDragListener());
    findViewById(R.id.bottomright).setOnDragListener(new MyDragListener());

  }

  private final class MyTouchListener implements OnTouchListener {
    public boolean onTouch(View view, MotionEvent motionEvent) {
      if (motionEvent.getAction() == MotionEvent.ACTION_DOWN) {
        ClipData data = ClipData.newPlainText("", "");
        DragShadowBuilder shadowBuilder = new View.DragShadowBuilder(view);
        view.startDrag(data, shadowBuilder, view, 0);
        view.setVisibility(View.INVISIBLE);
        return true;
      } else {
        return false;
      }
    }
  }

  class MyDragListener implements OnDragListener {
    Drawable enterShape = getResources().getDrawable(R.drawable.shape_droptarget);
    Drawable normalShape = getResources().getDrawable(R.drawable.shape);

    @Override
    public boolean onDrag(View v, DragEvent event) {
      int action = event.getAction();
      switch (event.getAction()) {
      case DragEvent.ACTION_DRAG_STARTED:
        // Do nothing
        break;
      case DragEvent.ACTION_DRAG_ENTERED:
        v.setBackgroundDrawable(enterShape);
        break;
      case DragEvent.ACTION_DRAG_EXITED:
        v.setBackgroundDrawable(normalShape);
        break;
      case DragEvent.ACTION_DROP:
        // Dropped, reassign View to ViewGroup
        View view = (View) event.getLocalState();
        ViewGroup owner = (ViewGroup) view.getParent();
        owner.removeView(view);
        LinearLayout container = (LinearLayout) v;
        container.addView(view);
        view.setVisibility(View.VISIBLE);
        break;
      case DragEvent.ACTION_DRAG_ENDED:
        v.setBackgroundDrawable(normalShape);
      default:
        break;
      }
      return true;
    }
  }
}

If you start this Activity you should be able to drag the ImageViews to another container.