Testing that button starts an Activity with Robolectric

Use Robolectric's StartedMatcher

@RunWith(Test9Runner.class) 
public class MainActivityTest  {
    private MainActivity activity;
    private Button pressMeButton;

    @Before
    public void setUp() throws Exception 
    {
        activity = new MainActivity();
        activity.onCreate(null);
        pressMeButton = (Button) activity.findViewById(R.id.button1);
    }

    @Test
    public void shouldStartNextActivityWhenButtonIsClicked() 
    {
        pressMeButton.performClick();
        assertThat(activity, new StartedMatcher(NextActivity.class));
    }  
}

Inspired by @MichK's answer, here is a complete running test using the buildActivity method chain from Robolectric 2.2+:

@Test
public void testStartScheduleActivity() {
    HomeScreenActivity homeActivity = Robolectric.buildActivity(HomeScreenActivity.class).create().start().visible().get();
    ShadowActivity shadowHome = Robolectric.shadowOf(homeActivity);
    Button btnLaunchSchedule = (Button) homeActivity.findViewById(R.id.btnLaunchSchedule);
    Robolectric.clickOn(btnLaunchSchedule);

    assertThat(shadowHome.peekNextStartedActivityForResult().intent.getComponent(), equalTo(new ComponentName(homeActivity, ScheduleActivity.class)));
}

In Robolectric 2.1.1 you can verify if Intent starting new Activity was emitted in following way.

@RunWith(RobolectricTestRunner.class)
public class MyTest {
  private ShadowActivity shadowActivity;
  private MyActivity activity;

  @Before
  public void setup() {
    activity = new MyActivity();
    shadowActivity = Robolectric.shadowOf(activity);        
  }

  @Test
  public shouldStartNewActivityWhenSomething() {
    //Perform activity startup
    //Do some action which starts second activity, for example View::performClick()
    //...
    //Check Intent
    Intent intent = shadowActivity.peekNextStartedActivityForResult().intent;
    assertThat(intent.getStringExtra(MySecondActivity.EXTRA_MESSAGE)).isEqualTo("blebleble");
    assertThat(intent.getComponent()).isEqualTo(new ComponentName(activity, MySecondActivity.class));
  }
}

This is similar to what I am doing. Please note that creating Activity by calling new Activity() will make Robolectric print warnings about creating activity improperly, this probably can be done better...

Updating this for 3.1.2 as the answers above did not work for me:-

    loginButton.callOnClick();

    Intent startedIntent = shadowOf(activity).getNextStartedActivity();
    ShadowIntent shadowIntent = shadowOf(startedIntent);
    assertEquals(NextActivity.class, shadowIntent.getIntentClass());