How can I change the number of products shown on an archive page?

There are two different ways to accomplish this.  

Change It Everywhere

If you'd like to make a global setting that affects ALL archive pages then you can use the "show at most" setting under WordPress' Settings → Reading page.

This affects all archives on your entire site, including EDD Product archives, Blog archives, and any custom post archive you may have.

Change It In One Place

EDD provides a shortcode called [downloads] which renders a product archive, and accepts a number for how many you'd like to show.  Here's a simple example:

[downloads number="15" columns="3"]

In-depth documentation on [downloads] is available here.