You can easily achieve that using groupBy() method of the Collection class, but mind that dateTime field won't qualify as array key, so you also need accessor for that:

$events->groupBy('simpleDate');

// returns something like this:
// array(
//   '2014-04-18' => array(
//     0 => object(Event)(
//       'incrementing' => true,
//       'timestamps' => true,
//       'exists' => true
//     ),
//     1 => object(Event)(
//       'incrementing' => true,
//       'timestamps' => true,
//       'exists' => true
//     )
//   ),
//   '2014-04-10' => array(
// .......


// Event model:
public function getSimpleDateAttribute()
{
  return substr($this->attributes['date'], 0, 10); // or whatever you like to process dateTime field
}