Google, and as far as I have been able to find, all other web search sites do not allow scraping in any form, including just finding the number of hits.
In fact I'm pretty sure that none even offer a web API to retrieve this info any more, at least not for free.
I realize this is a service that can be very easily abused, which is why it is not offered any more. But there are many other services which are offered various limits using API keys and throttling and quotas.
But I haven't been able to find a service for "web search hits" that's free, even with limits.
- Free, as in no fee.
- Registration, throttling, daily limits, any other kind of restriction is OK.
- Service with the fewest restrictions is, however, preferred over those with more restrictions.
- Service provided by or using Google is preferred, but other providers are OK.
- Any format is OK, though urlencoded and JSON are expected.
- Must be available live on-line of course!
- Batching strongly preferred.
(Ability to get the number of hits for two or many terms with one call.)
- Services with more "advanced search options" are preferred over services with fewer such options.
(Options such as restricting search to certain TLDs, supporting an "OR" operator, etc.)
One use case is doing first approximations of comparative popularity of synonyms or spelling variants. I'm sure there are plenty of other use cases.