Yes. There are a variety of ways to accomplish that. If you have a specific list of sites on the web you want to search, it's easy. If not, the usual approach is to use a free partner site such as www.master.com for a broad-based web search.
An alternative is to implement a "meta-search" against other search engines. Texis Web Script includes tools for setting that up. Note, however, that other search engines may or may not allow meta-searching.
If you seek to spider the entire web and build a proprietary web-search engine, Texis also is an excellent platform for that; however, such an undertaking takes considerable resources for bandwidth, machinery, administration, etc., and is normally not practical as a "sideline" or by a thinly funded start-up business.