I disagree on that.
Most users don't need nor understand the Standard (Advanced) Search Form.
So why making it more complicated for them when the simple Keyword Input is enough?
I had zero complaints from my Users (about 35K at the moment) when we Implemented the dropdowns - in fact we got many congrats about the much cleaner/easier layout.
I didn't say anything regarding the 'advanced search' ... my point is that the search function should be easily accessible and visible to everyone.
The search function shouldn't be hidden.
You shouldn't make your users 'search' for it.
In fact, it should be the first thing that is VISIBLE on your site. That...and a link to your site map.
The key here is to provide the standard site tools in a usable manner so that your new and existing users can enjoy your site.
Just think about it for a moment...
A new user visits your site...
They have questions but would rather search first -- Where is the search function?
Do you have one?
It's not visible?
Wait, they don't give up there ... they start looking for a "search" link starting from the top.
They find one. But are disappointed that it's not on the page.
They click on the link.
IT'S A DROP DOWN!
I'm not sure about you but at this point why not direct user to serch page? You made them do all this work. For what? A dropdown.
Now, if they want to use the advanced search they will have to click another link.
What do you think is easier?
Search for link / click a link for a dropdown / input / submit
OR
Input / submit