bbPress Membership levels, Basic, Premium and Lifetime Premium. Based on some codes in bbPress forums.

functions.php

<?php

function my_custom_get_dynamic_roles( $bbp_roles )
{
  /* Add a role called Community Contributor */
	$bbp_roles['bbp_basic_member'] = array(
		'name' => 'Basic Member',
		'capabilities' => my_custom_get_caps_for_role( 'bbp_basic_member' )
		);
	
		/* Add a role called Community Contributor */
	$bbp_roles['bbp_premium_member'] = array(
		'name' => 'Premium Member',
		'capabilities' => my_custom_get_caps_for_role( 'bbp_premium_member' )
		);
	
		/* Add a role called Community Contributor */
	$bbp_roles['bbp_lifetime_premium_member'] = array(
		'name' => 'Lifetime Premium Member',
		'capabilities' => my_custom_get_caps_for_role( 'bbp_lifetime_premium_member' )
		);
		
	return $bbp_roles;
}

add_filter( 'bbp_get_dynamic_roles', 'my_custom_get_dynamic_roles', 1 );

function my_custom_get_caps_for_role_filter( $caps, $role )
{
	/* Only filter for roles we are interested in! */
	if( $role == 'bbp_participant' || $role == 'bbp_community_contributor' || $role == 'bbp_basic_member' || $role == 'bbp_premium_member' || $role == 'bbp_lifetime_premium_member')
		$caps = my_custom_get_caps_for_role( $role );

	return $caps;
}

add_filter( 'bbp_get_caps_for_role', 'my_custom_get_caps_for_role_filter', 10, 2 );

function my_custom_get_caps_for_role( $role )
{
	switch ( $role )
	{
		/* Disable viewing of private forums by 'Participants' */
		case 'bbp_participant':
			return array(

				// Primary caps
				'spectate'              => true,
				'participate'           => true,
				'moderate'              => false,
				'throttle'              => false,
				'view_trash'            => false,

				// Forum caps
				'publish_forums'        => false,
				'edit_forums'           => false,
				'edit_others_forums'    => false,
				'delete_forums'         => false,
				'delete_others_forums'  => false,
				'read_private_forums'   => false,
				'read_hidden_forums'    => false,

				// Topic caps
				'publish_topics'        => true,
				'edit_topics'           => true,
				'edit_others_topics'    => false,
				'delete_topics'         => false,
				'delete_others_topics'  => false,
				'read_private_topics'   => false,

				// Reply caps
				'publish_replies'       => true,
				'edit_replies'          => true,
				'edit_others_replies'   => false,
				'delete_replies'        => false,
				'delete_others_replies' => false,
				'read_private_replies'  => false,

				// Topic tag caps
				'manage_topic_tags'     => false,
				'edit_topic_tags'       => false,
				'delete_topic_tags'     => false,
				'assign_topic_tags'     => true,
			);
			break;
			
		/* Capabilities for 'Basic Member' */
		case 'bbp_basic_member':
			return array(
				// Primary caps
				'spectate'              => true,
				'participate'           => true,
				'moderate'              => false,
				'throttle'              => false,
				'view_trash'            => false,

				// Forum caps
				'publish_forums'        => false,
				'edit_forums'           => false,
				'edit_others_forums'    => false,
				'delete_forums'         => false,
				'delete_others_forums'  => false,
				'read_private_forums'   => false,
				'read_hidden_forums'    => false,

				// Topic caps
				'publish_topics'        => true,
				'edit_topics'           => true,
				'edit_others_topics'    => false,
				'delete_topics'         => false,
				'delete_others_topics'  => false,
				'read_private_topics'   => false,

				// Reply caps
				'publish_replies'       => true,
				'edit_replies'          => true,
				'edit_others_replies'   => false,
				'delete_replies'        => false,
				'delete_others_replies' => false,
				'read_private_replies'  => false,

				// Topic tag caps
				'manage_topic_tags'     => false,
				'edit_topic_tags'       => false,
				'delete_topic_tags'     => false,
				'assign_topic_tags'     => true,
			);
			break;
			
			
		/* Capabilities for 'Premium Member' */
		case 'bbp_premium_member':
			return array(
				// Primary caps
				'spectate'              => true,
				'participate'           => true,
				'moderate'              => false,
				'throttle'              => false,
				'view_trash'            => false,

				// Forum caps
				'publish_forums'        => false,
				'edit_forums'           => false,
				'edit_others_forums'    => false,
				'delete_forums'         => false,
				'delete_others_forums'  => false,
				'read_private_forums'   => true,
				'read_hidden_forums'    => false,

				// Topic caps
				'publish_topics'        => true,
				'edit_topics'           => true,
				'edit_others_topics'    => false,
				'delete_topics'         => false,
				'delete_others_topics'  => false,
				'read_private_topics'   => false,

				// Reply caps
				'publish_replies'       => true,
				'edit_replies'          => true,
				'edit_others_replies'   => false,
				'delete_replies'        => false,
				'delete_others_replies' => false,
				'read_private_replies'  => false,

				// Topic tag caps
				'manage_topic_tags'     => false,
				'edit_topic_tags'       => false,
				'delete_topic_tags'     => false,
				'assign_topic_tags'     => true,
			);
			break;
			
			
		/* Capabilities for 'Lifetime Premium' */
		case 'bbp_lifetime_premium_member':
			return array(
				// Primary caps
				'spectate'              => true,
				'participate'           => true,
				'moderate'              => false,
				'throttle'              => false,
				'view_trash'            => false,

				// Forum caps
				'publish_forums'        => false,
				'edit_forums'           => false,
				'edit_others_forums'    => false,
				'delete_forums'         => false,
				'delete_others_forums'  => false,
				'read_private_forums'   => true,
				'read_hidden_forums'    => false,

				// Topic caps
				'publish_topics'        => true,
				'edit_topics'           => true,
				'edit_others_topics'    => false,
				'delete_topics'         => false,
				'delete_others_topics'  => false,
				'read_private_topics'   => false,

				// Reply caps
				'publish_replies'       => true,
				'edit_replies'          => true,
				'edit_others_replies'   => false,
				'delete_replies'        => false,
				'delete_others_replies' => false,
				'read_private_replies'  => false,

				// Topic tag caps
				'manage_topic_tags'     => false,
				'edit_topic_tags'       => false,
				'delete_topic_tags'     => false,
				'assign_topic_tags'     => true,
			);
			break;

		default :
			return $role;
	}
}

?>