Imagine if sites had a
<meta name="searchurl" value="http://example.com/search?query=%q" />
tag in their headers. This would allow agents to autodiscover and utilise a site's search engine if one was available simply by substituting %q for a url encoded query. There could even be a type="..." attribute that gave the mime type of the results - Atom would be good. Although that could just as easily be done with Accept headers and the other standard mechanisms for negotiating types.
Search engines could even use it to get better results from stuff like shopping and review sites.
Of course there's a possibility (nay, a probability even) that it'd be co-opted by spammers and also you have to ask yourself - why would sites provide this as a service and who would want to use it anyway so it's probably one for the "WTF were you thinking" file but hey ho.
I need more tea.
 Although it occurs to me that
<link rel="alternative" name="search" href="..." />
might work even better.