Can you help me discover the solution to removing .html from Magento category URL?
How configure magento such that the category url does not have “.html” in the url?

If you want to remove .html from all Magento’s category URL then Follow the below steps

1. Go to System -> Config -> Catalog -> Search Engine Optimizations tab
2. Delete “.html” from Category URL Suffix.
3. Go to System->Index Management
4. Reindex “Catalog URL Rewrites”
5. Refresh cache

If you want to remove  .html from all Magento’s product URL then steps will same. Except

2. Delete “.html” from Product URL Suffix.

Original link : http://www.blog.magentosupport.net/2011/07/remove-html-from-category-or-product-url-for-magento-webshop/