An implementation of the classic BuddyPress login form and logged in avatar,logout link provided as a widget.

hnla BP login form widget

add_action('widgets_init', create_function('', 'return register_widget("HNLA_loggin_Widget");') );

class HNLA_loggin_Widget extends WP_Widget {

  function __construct() {	
		parent::__construct(
			'HNLA_loggin_Widget',
			'BP Login, Logout form',
			array( 'description' => __('Displays the standard BP login form and logged in avatar, logout link', 'hnla'), )
		);
	}

	public function widget( $args, $instance ) {
		global $bp, $current_user, $wpdb;
		extract( $args );
  
		$title = apply_filters( 'widget_title', empty($instance['title']) ? '' : $instance['title'], $instance );
		
		echo $before_widget;
		
		// If we have an empty title field in the widget we'll remove the heading tag markup as well
		if( !empty( $title ) ) {
		echo $before_title .
		 	$title .
		  $after_title; 
		}
	 
 // Do our content to display ?>
	
  <div class="sidebar-login">
		<?php if( !is_user_logged_in() ) :?>
		<p id="login-text">
		<?php _e( 'To start connecting please log in first.', 'hnla' ) ?>
		</p>

		<?php if ( bp_get_signup_allowed() ) : ?>
			<?php printf( __( ' You can also <a href="%s" title="Create an account">create an account</a>.', 'hnla' ), site_url( BP_REGISTER_SLUG . '/' ) ) ?>
		<?php endif; ?>		
		
		<form name="login-form" id="sidebar-login-form" class="standard-form" action="<?php echo site_url( 'wp-login.php', 'login_post' ) ?>" method="post">
			<label><?php _e( 'Username', 'hnla' ) ?>
			<input type="text" name="log" id="sidebar-user-login" class="input focused" value="<?php if ( isset( $user_login) ) echo esc_attr(stripslashes($user_login)); ?>"  /></label>

			<label><?php _e( 'Password', 'hnla' ) ?>
			<input type="password" name="pwd" id="sidebar-user-pass" class="input" value=""  /></label>

			<p class="forgetmenot"><label><input name="rememberme" type="checkbox" id="sidebar-rememberme" value="forever"  /> <?php _e( 'Remember Me', 'hnla' ) ?></label></p>

			<?php do_action( 'bp_sidebar_login_form' ) ?>
			<input type="submit" name="wp-submit" id="sidebar-wp-submit" value="<?php _e('Log In'); ?>"  />
			<input type="hidden" name="testcookie" value="1" />
		</form>
		
		<?php else: ?>
		
		<div id="sidebar-me">
			<a href="<?php echo bp_loggedin_user_domain(); ?>">
				<?php bp_loggedin_user_avatar( 'type=thumb&width=40&height=40' ); ?>
			</a>

			<h4><?php echo bp_core_get_userlink( bp_loggedin_user_id() ); ?></h4>
			<a class="button logout" href="<?php echo wp_logout_url( wp_guess_url() ); ?>"><?php _e( 'Log Out', 'hnla' ); ?></a>

			<?php do_action( 'bp_sidebar_me' ); ?>
		</div>
		
		<?php endif; ?>
		
		</div><!-- // .sidebar-login -->
		
		<?php    
      
	echo $after_widget;
	// end markup generation
	
	} // close widget function

	public function update( $new_instance, $old_instance ) {
		$instance = $old_instance;
		$instance['title'] = strip_tags($new_instance['title']);
		return $instance;
	} 
	public function form( $instance ) {
		$instance = wp_parse_args( (array) $instance, array( 'title' => '') );
		$title = strip_tags($instance['title']);
  
  ?>
		<p>
  <label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?></label>
		<input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo esc_attr($title); ?>" />
  </p>
		<?php 
	}

}