I see categories as a key part of my site's organization system, with each indicating a section or specific topical area of the site. I use them the same way I would a menu-based navigation on a regular website, or how I would organize my files on my computer. I give a lot of thought to how categories are set up on my sites and rarely create them on the fly.
I use tags as a way to further optimize my content with keyword phrases relevant to the article. I try to use the same tags whenever it makes sense, as a way to help users find other similar articles. I create new tags as needed, and try to tag all articles with as many (relevant) tags as possible.
I hope that helps!
Magical Mama, joyfully home educating my three wonders: FR (12/02), EG (05/05), DK (06/09)