[susan53]

The language is changing. My original reaction was to say : No - you need the preposition. You could say either,

He searched for the answer on the Internet.
He searched the internet for the answer.

but in each case "for" must be used.

I was convinced. However, given that you should never trust your own intuition about language, I checked it anyway, and found loads of examples like :

This site allows you to search information on current funding programmes (UK site)
Use * to search words with different letters (e.g. wom*n). (UK site)
the search boxes offer the opportunity to search Accommodation (by keyword, price and region). (NZ site)
To search accommodation and flights online... (US site)

Interestingly, the context was always connected with the internet. In other contexts (at least all the ones I checked) for was always used - eg :

Police and Johannesburg metro police officers knocked on each door in extension six as they searched for stolen goods

So : my conclusion would be that when you're looking for information of some sort on the internet, then either are possible. If you're talking about something else, use for.

At the moment anyway. The change is likely to spread...