Google search over SSL works for web search, but since Google has a unified interface for search, it also works for video search, book search, blog search, news search. You won't be able to use image search, product search and Google Maps, which aren't yet properly integrated with the new Google interface.
The main benefit of using the SSL version of Google search is that the communication between your computer and Google's servers is encrypted. This is especially useful if you're using a public computer, an open WiFi network or you're using Google for sensitive searches. An interesting side-effect is that browsers no longer send referrals when you're clicking on search results that don't use SSL.
Google Secure Search has a special logo, which never changes for special occasions, and the URL is https://www.google.com.
I used WireShark, a free packet sniffer, to compare the standard HTTP interface with the new HTTPS version. As you can see, if you use Google Search over SSL, even the URL is encrypted, so your query is a secret for everyone, except Google:
If you'd like to use Google SSL as the default search engine in Chrome, go to the Settings dialog, click on the "Manage" button next to the list of search engines, add "Google SSL" and make it the default search engine. The downside is that Google Chrome will no longer show suggestions when you type your query. Google Chrome should use this in the incognito mode.
For Firefox, try this search plug-in, while for Internet Explorer, you can create a search provider using the URL: https://www.google.com/search?q=TEST.
{ via Google Blog }