One thing that I would like from Google searches that I do not have is not too complicated. A front-end that is designed to digest my multi-search needs.
e.g. Let's say I am searching on some new software, I would like to be able to limit the search to a number of domains, like DonationCoder, Lifehackers, Wilders, Snapfiles, MajorGeeks, Fileforum, Freewaregenius and maybe another 5 or 10 other domains. (And often a review or discussion in one of those will link to other good discussions.) Afaik, there is no direct way to do that in Google (you can ask for one domain) however a front-end could conceivably do this. Even if it adds a couple of seconds, no problemo, a really focused search. Remember and name my lists, let me add a new domain quickly when needed, and fly.
There are probably many other similar "front-end" enhancements that could come to mind (the built-in Boolean in Google is quite powerful but even that might sometimes use a front-end, or even "save-searches" options). This one about domains I will use as an example. (Note: All this does not mean that I will not also do the "full search" .. that is how you find new gems, yet often you want to cut right to the quick.)
Sidenote: I got an email today from the very well-respected xplorer² where he specifically mentions a toolbar.
"google beater!! Naturally it will make your internet searches more convenient but that's not all. It will help you make sense of the search results with keyword highlighting and in-page searches. And it is also giving you access to all your online e-mail accounts (hotmail, yahoo, gmail etc) with a single click!"
However I am not sure if there is much there of great help, look forward to giving it a try.
Oh, one other point. The biggest lack in my browser searches is the inability to have two or three "Find"s active at one time, each one with their own button, able to move back and forth without a retyping. It would be a natural Firefox extension -- yet does not seem to exist, I asked over in that realm once. Anybody have any thoughts ? I really like the Firefox-Linkman-Powermarks incremental-letter search (any duplicate of that on Opera or Chrome ?) sitting down in the bar at bottom in Firefox, never needing a ctrl-f. Excellent, simple design. However there is plenty of room there, why not two or three "Find" fields ?
Feel free to break out these last two sections into their own thread, if they are of solid interest.