Buttons in input groups are a bit different and require one extra level of nesting. Instead of .input-group-addon, you'll need to use .input-group-btn to wrap the buttons. This is required due to default browser styles that cannot be overridden.

<div class="row">
  <div class="col-lg-6">
    <div class="input-group">
      <span class="input-group-btn">
        <button class="btn btn-default" type="button">Go!</button>
      </span>
      <input type="text" class="form-control" placeholder="Search for...">
    </div><!-- /input-group -->
  </div><!-- /.col-lg-6 -->
  <div class="col-lg-6">
    <div class="input-group">
      <input type="text" class="form-control" placeholder="Search for...">
      <span class="input-group-btn">
        <button class="btn btn-default" type="button">Go!</button>
      </span>
    </div><!-- /input-group -->
  </div><!-- /.col-lg-6 -->
</div><!-- /.row -->

Related classes: