Interesting question. I would posit that, generally speaking, numbering the results assigns more importance to the order than is actually merited and unnecessarily clutters the results.
It's purely a guess (I would love to see research to prove/disprove my theory), but I suspect that numbering the results would increase the user's cognitive load because they now have to think about the numbering and what it might mean for them. E.g. instead of picking what is most relevant to their needs, they're also needing to worry about why the result that seemed most useful to them is ranked below 5 other items. Without the numbers, I would guess that this is less of a factor.
Likewise, the goal of any site search is to drive traffic to the resultant pages (you don't want people just hanging out on the results page; you want them to migrate to your actual content). Every non-functional element added to the page clutters and distracts from the primary objective, which is to move the user forward.
The only case where I would consider using numbering on search results is if the numbers actually having meaning in context. E.g. if I search for a product and fort by 'best reviewed', it might be useful to know that a product is the #1 best reviewed vs. the #5 best reviewed. However, even in that case, I'd rather the user sees the real rating in the summary, not just the relative result rank.