This is a complete solution. I’ve just updated this example code with the information provided in the answer below by @mad. Also check the solution below from @Khobaib explaining how to deal with picasa images.

Update

I’ve just reviewed my original answer and created a simple Android Studio project you can checkout from github and import directly on your system.

https://github.com/hanscappelle/SO-2169649

(note that the multiple file selection still needs work)

Single Picture Selection

With support for images from file explorers thanks to user mad.

public class BrowsePictureActivity extends Activity {

    // this is the action code we use in our intent, 
    // this way we know we're looking at the response from our own action
    private static final int SELECT_PICTURE = 1;

    private String selectedImagePath;

    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);

        findViewById(R.id.Button01)
                .setOnClickListener(new OnClickListener() {

                    public void onClick(View arg0) {

                        // in onCreate or any event where your want the user to
                        // select a file
                        Intent intent = new Intent();
                        intent.setType("image/*");
                        intent.setAction(Intent.ACTION_GET_CONTENT);
                        startActivityForResult(Intent.createChooser(intent,
                                "Select Picture"), SELECT_PICTURE);
                    }
                });
    }

    public void onActivityResult(int requestCode, int resultCode, Intent data) {
        if (resultCode == RESULT_OK) {
            if (requestCode == SELECT_PICTURE) {
                Uri selectedImageUri = data.getData();
                selectedImagePath = getPath(selectedImageUri);
            }
        }
    }

    /**
     * helper to retrieve the path of an image URI
     */
    public String getPath(Uri uri) {
            // just some safety built in 
            if( uri == null ) {
                // TODO perform some logging or show user feedback
                return null;
            }
            // try to retrieve the image from the media store first
            // this will only work for images selected from gallery
            String[] projection = { MediaStore.Images.Media.DATA };
            Cursor cursor = managedQuery(uri, projection, null, null, null);
            if( cursor != null ){
                int column_index = cursor
                .getColumnIndexOrThrow(MediaStore.Images.Media.DATA);
                cursor.moveToFirst();
                String path = cursor.getString(column_index);
                cursor.close();
                return path;
            }
            // this is our fallback here
            return uri.getPath();
    }

}

Selecting Multiple Pictures

Since someone requested that information in a comment and it’s better to have information gathered.

Set an extra parameter EXTRA_ALLOW_MULTIPLE on the intent:

intent.putExtra(Intent.EXTRA_ALLOW_MULTIPLE, true);

And in the Result handling check for that parameter:

if (Intent.ACTION_SEND_MULTIPLE.equals(data.getAction()))
        && Intent.hasExtra(Intent.EXTRA_STREAM)) {
    // retrieve a collection of selected images
    ArrayList<Parcelable> list = intent.getParcelableArrayListExtra(Intent.EXTRA_STREAM);
    // iterate over these images
    if( list != null ) {
       for (Parcelable parcel : list) {
         Uri uri = (Uri) parcel;
         // TODO handle the images one by one here
       }
   }
} 

Note that this is only supported by API level 18+.