Here's a feature, let me add weight to my search results. I want to give preference to stackoverflow, HN, reddit, etc. I don't want to limit my search to only those sites, but I'd like to push them a little closer to the top. Also, let me setup a blacklist of sites to exclude. I don't want to see expertexchange... ever. I should be able to share my custom search setup with others, kind of like how AdBlock has subscriptions, I could select popular setups, or build my own.
And, what if I could select my settings in a dropdown when searching. So, maybe the people at HN setup a whitelist of 100 of the best sites for programming help. I add this list to my account. Now, anytime I want to search for a programming question, I type in the query, select my custom search type from the dropdown, 'programming questions', and then click search. I'll only get results from those 100 sites.
Google will never implement this for a variety of reasons, so it's room for competition.