This is factually incorrect.

Google has replaced the "Web Search API" with the "Google Custom Search API" (Custom Search Engine = CSE): http://code.google.com/apis/customsearch/docs/dev_guide.html

When you initially setup CSE you need to specify at least once site to search, but afterwards you can remove this restriction.

The API is limited to 100 calls per day by default, but you can ask for more. The old API would cut you off if you used it excessively from outside a web browser. The older SOAP API had a hard limit (I think 1000 calls?)