Gary Jones

If bots are attacking your site by appending <code>/search/a-random-string-or-word</code>, then those pages may be getting indexed by search engines, or populating search logs.
This plugin disables that permalink structure.
Search forms will still work, and the search results page will use the less index-friendly <code>?s=search-term</code> format.

Disable Search Slug

Stops /search/... URLs from working, resulting in a WordPress 404 page not found.

craigsimps

This is a super-simple plugin which will turn WordPress’ default <code>/?s=query%20terms</code> into <code>/search/query+terms/</code> if you have pretty permalinks enabled.
This is something which I have been placing into a theme include or in a core functionality plugin until recently, but it makes sense to separate this functionality out into an individual plugin so it can be switched on and off independently.
The plugin has no administrative interface or control panel. Activation turns it on, deactivation turns it off. Once activated, performing a search using the standard WP search widget should give you a much nicer search URL.

Simple Search Rewrite

Redirects search results from /?s=query to /search/query/, and converts %20 to +.

Disable Search Slug vs Simple Search Rewrite