1. Results aren't counted. Maybe I look at the first 100 results and I want to see how well a certain site is ranked. Yahoo Search does that.
2. Google hasn't eliminated near-duplicate documents from the index, and you can see a news that appears in many sites with almost identic content and that is shown in the top 10 results duplicated.
3. Google should have an easy-to-access page where you can search without localization and personalization. For example, http://www.google.com/nlp.
4. If I mentioned about NLP (natural language processing), Google should have a way to process the query in order to search using the most relevant keywords. If I search for [Sony Ericsson K750i customization], Google should also query for [Sony Ericsson K750i personalization] or [Sony Ericsson K750i accessories].
5. There is no easy way to view only the pages updated yesterday or last week.
6. You can't restrict the search to pages that have a certain size, let's say over 200KB.
8. Google doesn't have an option to view a page only as text, without images, scripts, or navigation. They do that for mobile search and it's really useful if you just want to skim through the text.
9. You can't use the site operator multiple times. Maybe you want to search something in three sites. It should something like: [nlp site:slashdot.org site:digg.com site:bbc.co.uk].
10. Google should also show high-quality sites that fit in the same domain as your query, but they aren't extremely relevant for your query. If you search for [Sony Ericsson K750i reviews], Google should show at the bottom of the page two or three sites about mobile phone reviews.
25 things I hate about Google [Search Engine Watch]