There are two ways to do this.
1. Image by image: Insert the image, switch to the HTML tag, locate the image code which will look something like this:
<img width="480" height="320" alt="" src="http://timeentertainment.files.wordpress.com/2011/12/new-years-eve-poster-horizontal.jpg?w=480&h=400&crop=1&h=320" title="New Year's Eve" class="aligncenter">
Add style="border: none; background: none;" right after img in the code as I show below.
<img style="border: none; background: none;" width="480" height="320" alt="" src="http://timeentertainment.files.wordpress.com/2011/12/new-years-eve-poster-horizontal.jpg?w=480&h=400&crop=1&h=320" title="New Year's Eve" class="aligncenter">
2. With the Custom Design upgrade, you can add the following to the CSS edit window and take care of it once and for all and not have to do it for each image.
.hentry img, body.attachment .navigation img {
border: none;
background: none;
}