How to put border on a selected item in the ListView?

Follow these steps:

1 - Add the attribute android:choiceMode to ListView ,

to allow you to select only one line:

android:choiceMode="singleChoice"

to allow you to select more than one line:

android:choiceMode="multipleChoice"

To customize the appearance of the selection requires a Chooser.

2 - Create the draw / drawable folder to use in the Chooser:

list_item_selected.xml

<?xml version="1.0" encoding="utf-8"?>

<shape xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle" >

        <solid android:color="cor do fundo quando selecionado"/>
        <stroke 
            android:color="cor da borda quando selecionado"
            android:width="3dip"/>
</shape>

list_item_unselected.xml

<?xml version="1.0" encoding="utf-8"?>

<shape xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle" >

        <solid android:color="cor do fundo quando não selecionado"/>
        <stroke 
            android:color="cor da borda quando não selecionado"
            android:width="3dip"/>
</shape>

Put the colors to your liking! If in any case you want the color to be the one at the bottom of the ListView use @android:color/transparent

3 - Create the Chooser:

list_item_selector.xml

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

   <item android:drawable="@drawable/list_item_selected" android:state_pressed="true"/>
   <item android:drawable="@drawable/list_item_selected" android:state_selected="true"/>
   <item android:drawable="@drawable/list_item_selected" android:state_activated="true"/>

    <!-- não seleccionada -->
    <item android:drawable="@drawable/list_item_unselected"/>
</selector> 

4 - Assign the Selector to the item of the list:

android:background="@drawable/list_item_selector"

Note: I did not test, I hope I was not mistaken.