$userModel = new UserModel();
        $userModel->mycustomfield = 'test value';
        craft()->users->saveUser($userModel);

Internal Server Error
Property "CraftUserModel.mycustomfield" is not defined.

$user = craft()->userSession->getUser();
        $userModel = new UserModel();
        $userModel->id = $user->id;
        $userModel->getContent()->setAttributes(array(
            'mycustomfield' => 'my field value'
        ));
        craft()->users->saveUser($userModel);

$userModel->getContent()->mycustomfield = 'my value';

$user = craft()->userSession->getUser();
    $userModel = new UserModel();
    $userModel->id = $user->id;
    $userModel->username = $user->username;
    $userModel->email = $user->email;
    $userModel->password = '';
    $userModel->getContent()->mycustomfield = 'my custom value';
    $success = craft()->users->saveUser($userModel);
    if (!craft()->users->saveUser($userModel))
    {
        $errors = $userModel->getErrors();
    }

$userModel->getContent()->setAttributes(array(
    'mycustomfield' => 'my field value'
));

if (!craft()->users->saveUser($userModel))
{
    $errors = $userModel->getErrors();
}

craft()->users->getUser();

$user = craft()->userSession->getUser();
$user->getContent()->mycustomfield = 'my custom value';
$success = craft()->users->saveUser($user);
if (!craft()->users->saveUser($user))
{
    $errors = $user->getErrors();
}