Virtually all Wordpress blogs allow you to customs the sidebars of your blog using the various widgets that are available. One of these widgets is a search box. Instead of using the Wordpress widget you may want to consider using a Google Search Box linked to your Google Adsense account. Providing you also use categories to index your posts, visitors will still be able to find the information they want on your blog.

If they can’t find what they want and are going to click away from your site, you may as well get paid for it.

I mainly use Wordpress but I don’t see any reason why you couldn’t use the Google Search Box on other types of blogs such as Blogger providing they let you add HTML snippets.