That depends upon the tag and what you want to do with it. Where possible, I'd suggest adding your modification on top of the current tag's output in functions.php and then calling your new function in place of the original tag. But just to add to the complexity, there are some tags that call actually call a series of filters - in which case you can add a new filter to the end of that queue.
http://codex.wordpress.org/Function_Reference/add_filter
For example, to increase the number of words displayed by the_excerpt() from 55 to 100, you could use:
// Increase excerpt length
function my_excerpt_length($length) {
return 100; // Or whatever you want the length to be.
}
add_filter('excerpt_length', 'my_excerpt_length');
and then call <?php the_excerpt();?> in your template.