Category pages or archives? If you’re a little more specific you will probably get multiple ideas, but in general, if you’ve got a loop you can use one of the two following functions:
<?php the_excerpt(); ?>will show the custom or default excerpt for the post<?php the_content('Read More »'); ?>will show the full post with a “Read More” link employed if you’ve used<!-- more-->in your post to show only part of the post on aggregate templates
If you are looking for simple functions for your templates to display content, you should probably read up on the WordPress codex.