I assume they do, but looking for it is confusing due to all kinds of other APIs and tools they seem to offer.
All I want to do is issue a web request and receive a JSON or XML response containing Google's standard search results, and be able to page through them with new requests, etc.
Where can I find this?
like this? http://code.google.com/apis/ajaxsearch/
I think restful api is available too.
No, not any more, if by "basic" you mean a non-AJAX one. They continued to support the original SOAP API for people who got a key to use it years ago (I have one) until very recently, but it has been discontinued in favour of the AJAX Search.
You can experiment with the Google AJAX Search API and see some good samples at the Google Code Playground.