Selected answers from the Dumb SEO Questions G+ community.
Alan Bleiweiss: Those links are called "SiteLinks". Google decides which pages to place there based on the query and which pages Google believes are the strongest value pages of the site.
If you want category pages to show up, you need to boost the SEO value understanding of those categories. Even then, there is no guarantee Google will use those pages for those links.
Dave Elliott: Having a loogical site architecture including navigation and breadcrumbs(marked up with schema) is about all you can do.
Gerry White: Yep - it takes a a while and developing a brands the only way ...
Michael Martinez: If you are using SEO plugins, be sure they are NOT adding "noindex" to your category pages. Some do that by default. ADDENDUM: Some "SEO friendly" themes also do this.