Uploading an avatar fails when open_basedir restrictions are in effect. This can be fixed by adding a check for open_basedir restrictions in file /includes/functions_upload.php on line 834, which reads:

$tmp_path = (!@ini_get('safe_mode') || strtolower(@ini_get('safe_mode')) == 'off') ? false : $phpbb_root_path . 'cache';

All that needs to be done is replace that line with the following one:

$tmp_path = (@ini_get('open_basedir') || @ini_get('safe_mode') || strtolower(@ini_get('safe_mode')) == 'on') ? $phpbb_root_path . 'cache' : false;

Please see the following discussion for more information: http://www.phpbb.com/community/viewtopic.php?f=46&t=2131427