List multiple categories

Hello, I currently am categorizing each post in numerous categories and was hoping to display more than one category in each page template. Currently this is the code I use that shows only a single category that I have listed:
<a href="<?php $category = get_the_category(); echo get_category_link($category[0]->cat_ID); ?>"><?php echo $category[0]->cat_name; ?></a>

Any suggestions for how to show all categories? Also, I use other taxonomies, such as “motivations” – would I just replace the word “category” with “motivation” in order to retrieve a list of the “motivations” that each post is listed under?

Thank you!
Shawn