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Search the current site
Some Chrome extensions do little you couldn't otherwise do, but they save a little time. Search the current site is like that. All it does is present a little box where you can type in your search query, then send that search query to google with "site:thesiteyouron.com" prepended to the query (where, of course, thesiteyouron.com is actually the site you're on).
It's not like you couldn't do that yourself, but it's a quick timesaver, especially if you don't really want to extract the domain name from the omnibox prior to doing a search.
How often used: A few times a week.
Live without it factor: I could certainly live without it, but it's helpful to have around to save a few clicks, cuts, and pastes.