How can I increase the number of related products shown on my product page?

To increase the number of products shown in "Related Products", open up Themes > Template Editor > product.liquid.  Around line 225, you'll see this:

            {% for product in collection.products limit:5 %}

Increase the '5' to however many products you want to show in related products. Keep it to a multiplier of 4+1, so it's even.  For example, you could use 5, 9, 13, 17, 21, and so on.