Can I remove TIMES?

Use CSS to hide the times. Find the div ID or class and create a CSS property such as "display: none;"

There are several ways to configure the time...

(1) Alter the way time is displayed by default in Drupal with:
?q=admin/settings/event/timezone
?q=admin/settings/date-time

(2) Within the theme you can also further customize the time display for your events. Take a look at the event.theme for all of the themable functions. For example, I changed the default display for the list of "upcoming" events because I wanted to show the start date, not the days before an event. This snippet goes into your template.php file for your theme.

 function THEMENAME_event_upcoming_item($node) {
  $output .= '<span class="event-timeleft">'. format_date($node->event_start, 'custom', 'l, M. j', $node->start_offset) .'</span>';
  $output .= l($node->title, "node/$node->nid", array('title' => $node->title));
  return $output;
} 

This snippet, on the other hand, is for the actual "node" display of an individual event item:

 function THEMENAME_event_nodeapi($node) {
  $output .= '<div class="event-nodeapi"><div class="'. $node->type. '-start">';
  $output .= '<label>'. t('Date: ') .'</label>'. format_date($node->event_start, 'custom', 'l F j, Y', $node->start_offset) .'</div></div>'."\n";
  $output .= '<div class="event-nodeapi"><div class="'. $node->type. '-start"><label>'. t('Start: ') .'</label>'. $node->start_time_format .'</div></div>'."\n";
  if ($node->event_start != $node->event_end) {
  $output .= '<div class="event-nodeapi"><div class="'. $node->type. '-end"><label>'. t('End: ') .'</label>'. $node->end_time_format.'</div></div>'."\n";
  }
  return $output;
} 

(etc for each of the different themable functions that control the different outputs)

Of course to completely remove the times, you would alter these functions and delete the lines where the time is printed to the page.

Ideally, the "has time" setting should disable the output of times when a node is rendered (only the date would be shown). This is work in progress.

Event for Drupal 8 is unrelated to older versions. If an issue similar to this one exists, please open a new issue with the 8.x branch.