Open up
/templates/base/scripts/BxBaseProfileView.php

find:
$ret = '<div class="menuBlock">';
$ret .= '<div class="menu_item_block">';
$ret .= '<div class="menu_item_block_left">';
$ret .= $oTemplMenu -> getActionsMenuItem( 'action_send.gif', _t('_SendLetter'), "compose.php?ID=$profileID" );
$ret .= $oTemplMenu -> getActionsMenuItem( 'action_fave.gif', _t('_Fave'), "javascript:void(0);", '', '', see more "window.open( 'list_pop.php?action=hot&amp;ID=$profileID', '', 'width={$this -> oTemplConfig -> popUpWindowWidth},height={$this -> oTemplConfig -> popUpWindowHeight},menubar=no,status=no,resizable=no,scrollbars=yes,toolbar=no,location=no' );" );
//$ret .= $oTemplMenu -> getActionsMenuItem( 'action_friends.gif', _t('_Befriend'),"javascript:void(0);", '', '', "window.open( 'list_pop.php?action=friend&amp;ID=$profileID', '', 'width={$this -> oTemplConfig -> popUpWindowWidth},height={$this -> oTemplConfig -> popUpWindowHeight},menubar=no,status=no,resizable=no,scrollbars=yes,toolbar=no,location=no' );" );
$ret .= $oTemplMenu -> getActionsMenuItem( 'action_greet.gif', _t('_Greet'), "javascript:void(0);", '', '', "window.open( 'greet.php?sendto=$profileID', '', 'width={$this -> oTemplConfig -> popUpWindowWidth},height={$this -> oTemplConfig -> popUpWindowHeight},menubar=no,status=no,resizable=no,scrollbars=yes,toolbar=no,location=no' );" );
//$ret .= $IMNow;
....etc...etc

comment out what you don't want to show such as:
//$ret .= $oTemplMenu -> getActionsMenuItem( 'action_music.gif', $this->getLinkStat('prMusic', _t('_ProfileMusic'), $profileID), "javascript:void(0);", '', '', "openRayWidget( 'mp3', 'player', '$profileID', '" . getPassword( $memberID ) . "', '$memberID');");

For profile music. Save the changes. Comment out any others.

Commenting out is just adding:
//

Before the code.

By commenting out rather than removing it totally you can simply remove the commenting(//) if you wish to re-enable at a later time.