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+.

Here is an update to the fine code that hcpl posted. but this works with OI file manager, astro file manager AND the media gallery too (tested). so i guess it will work with every file manager (are there many others than those mentioned?). did some corrections to the code he wrote.

public class BrowsePicture extends Activity {    //YOU CAN EDIT THIS TO WHATEVER YOU WANT    private static final int SELECT_PICTURE = 1;    private String selectedImagePath;    //ADDED    private String filemanagerstring;    public void onCreate(Bundle savedInstanceState) {        super.onCreate(savedInstanceState);        setContentView(R.layout.main);        ((Button) 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);            }        });    }    //UPDATED    public void onActivityResult(int requestCode, int resultCode, Intent data) {        if (resultCode == RESULT_OK) {            if (requestCode == SELECT_PICTURE) {                Uri selectedImageUri = data.getData();                //OI FILE Manager                filemanagerstring = selectedImageUri.getPath();                //MEDIA GALLERY                selectedImagePath = getPath(selectedImageUri);                //DEBUG PURPOSE - you can delete this if you want                if(selectedImagePath!=null)                    System.out.println(selectedImagePath);                else System.out.println("selectedImagePath is null");                if(filemanagerstring!=null)                    System.out.println(filemanagerstring);                else System.out.println("filemanagerstring is null");                //NOW WE HAVE OUR WANTED STRING                if(selectedImagePath!=null)                    System.out.println("selectedImagePath is the right one for you!");                else                    System.out.println("filemanagerstring is the right one for you!");            }        }    }    //UPDATED!    public String getPath(Uri uri) {        String[] projection = { MediaStore.Images.Media.DATA };        Cursor cursor = managedQuery(uri, projection, null, null, null);        if(cursor!=null)        {            //HERE YOU WILL GET A NULLPOINTER IF CURSOR IS NULL            //THIS CAN BE, IF YOU USED OI FILE MANAGER FOR PICKING THE MEDIA            int column_index = cursor            .getColumnIndexOrThrow(MediaStore.Images.Media.DATA);            cursor.moveToFirst();            return cursor.getString(column_index);        }        else return null;    }

hcpl's methods work perfectly pre-KitKat, but not working with the DocumentsProvider API. For that just simply follow the official Android tutorial for documentproviders: https://developer.android.com/guide/topics/providers/document-provider.html -> open a document, Bitmap section.

Simply I used hcpl's code and extended it: if the file with the retrieved path to the image throws exception I call this function:

private Bitmap getBitmapFromUri(Uri uri) throws IOException {        ParcelFileDescriptor parcelFileDescriptor =             getContentResolver().openFileDescriptor(uri, "r");        FileDescriptor fileDescriptor = parcelFileDescriptor.getFileDescriptor();        Bitmap image = BitmapFactory.decodeFileDescriptor(fileDescriptor);        parcelFileDescriptor.close();        return image;}

Tested on Nexus 5.