Most of the default Blogger templates display a white border and box shadow frame around every posted image like the example below:

But some bloggers prefer to have their images displayed without the border and shadow like so:

Method 1:
If you want to remove the borders from all of the images on your blog, add the following code to your CSS. Design > Template Designer > Advanced > Add CSS:
.post-body img, .post-body .tr-caption-container, .Profile img, .Image img, .BlogList .item-thumbnail img { border: 0px; -moz-box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); -webkit-box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); border-radius: 0px 0px 0px 0px; background: none; }
If you want to selectively remove the borders from specific images, add this code to your CSS.
Design > Template Designer > Advanced > Add CSS:
img.noborder { border: 0px; -moz-box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); -webkit-box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); box-shadow: 0px 0px 0px rgba(0, 0, 0, .0); border-radius: 0px 0px 0px 0px; background: none; }
<img class="noborder" src="http://YOURIMAGEURL">