The code below shows the “post-thumbnail” aka the featured image if the post has one, if not depending on the category, the default thumbnail is shown (with the comments, the code should be self-explanatory):
<?php
// If the post has a featured image defined use it
if( has_post_thumbnail() ) {
the_post_thumbnail();
// Default image for Technology category
} elseif ( is_category( 'technology' ) ) {
echo '<img src="' . get_bloginfo('template_directory') . '/images/default_technology_post_thumb.jpg" />';
// Default image for Gadgets category
} elseif ( is_category( 'gadgets' ) ) {
echo '<img src="' . get_bloginfo('template_directory') . '/images/default_gadgets_post_thumb.jpg" />';
// Default image for all others
} else {
echo '<img src="' . get_bloginfo('template_directory') . '/images/default_post_thumb.jpg" />';
}
?>
Suggested Reading: WordPress Codex — Conditional Tags