Remove padding from columns in Bootstrap 3

You'd normally use .row to wrap two columns, not .col-md-12 - that's a column encasing another column. Afterall, .row doesn't have the extra margins and padding that a col-md-12 would bring and also discounts the space that a column would introduce with negative left & right margins.

<div class="container">
    <div class="row">
        <h2>OntoExplorer<span style="color:#b92429">.</span></h2>

        <div class="col-md-4 nopadding">
            <div class="widget">
                <div class="widget-header">
                    <h3>Dimensions</h3>
                </div>
                <div class="widget-content">
                </div>
            </div>
        </div>

        <div class="col-md-8 nopadding">
            <div class="widget">
                <div class="widget-header">
                    <h3>Results</h3>
                </div>
                <div class="widget-content">
                </div>
            </div>
        </div>
    </div>
</div>

if you really wanted to remove the padding/margins, add a class to filter out the margins/paddings for each child column.

.nopadding {
   padding: 0 !important;
   margin: 0 !important;
}

Bootstrap 4 has added .no-gutters class.

Bootstrap 3.4 has added .row-no-gutters class

Bootstrap 3: I always add this style to my Bootstrap LESS / SASS:

.row-no-padding {
  [class*="col-"] {
    padding-left: 0 !important;
    padding-right: 0 !important;
  }
}

Then in the HTML you can write:

<div class="row row-no-padding">

If you want to only target the child columns you can use the child selector (Thanks John Wu).

.row-no-padding > [class*="col-"] {
    padding-left: 0 !important;
    padding-right: 0 !important;
}

You may also want to remove padding only for certain device sizes (SASS example):

/* Small devices (tablets, 768px and up) */
@media (min-width: $screen-sm-min) and (max-width: $screen-sm-max) {
  .row-sm-no-padding {
    [class*="col-"] {
      padding-left: 0 !important;
      padding-right: 0 !important;
    }
  }
}

You can remove the max-width part of the media query if you want it to support small devices upwards.