Drupal - How to hide a custom user field in user profile?

I think Field Permissions is what you are looking for. Here is a quote about it (from the module's project page):

... allows site administrators to set field-level permissions to edit, view and create fields on any entity.

Features:

• Enable field permissions on any entity, not just nodes.
• Role-based field permissions allowing different viewing patterned based on what access the user has.
• Author-level permissions allow viewing and editing of fields based on who the entity owner is.
• Permissions for each field are not enabled by default. Instead, administrators can enable these permissions explicitly for the fields where this feature is needed.
• Field permissions overview

To hide the field from the user profile form you can set the #access property of a field to FALSE using hook_form_FORMID_alter.

The following snippet hides the field field_organisation from the user profile form for non-admins:

function YOURCUSTOMMODULE_form_user_profile_form_alter(&$form, &$form_state, $form_id) {
  $current_user = user_uid_optional_load();
  if($current_user->uid != 1) {
    $form['field_organisation']['#access'] = FALSE;
  }
}

See also this similar question on drupalanswers

You can also hide the field from the user profile page (not the form) using template_preprocess_user_profile

The following snippet hides the field field_organisation from the user page for non-admins:

function YOURCUSTOMMODULE_preprocess_user_profile(&$vars) {
  $current_user = user_uid_optional_load();
  if($current_user->uid != 1) {
    unset($vars['user_profile']['field_organisation']);
  }
}