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Inspect element (built into Chrome)
As it turns out, the first extension I use quite a lot is the built-in function Inspect element, which you get to by right-clicking anywhere on a Web page. This replaces Firebug, which was an essential tool for developing and managing Web pages in Firefox.
Inspect element works just about as well, and it's always available.
How often used: I use this in spurts, when I'm doing Web development. Since that's not my full-time gig, it means I can go a month or more without using this.
Live without it factor: However, when I am doing Web development, this is absolutely critical and I couldn't live without it.
Chrome sync (built into Chrome)
I am constantly moving from machine to machine. I used to use Foxmarks (and then Xmarks), but like Firefox itself, Xmarks became quite cumbersome. Even so, syncing my bookmarks was necessary. Also, back on Firefox, I tried to keep my add-ons in sync, and so for a while I tried FEBE, but was never very happy with it.
Chrome sync, on the other hand, rocks the house. It syncs bookmarks and extensions seamlessly, without any hassle. It just works.
The only thing I don't like is how Chrome syncs bookmarks between desktop and mobile versions. The version of Chrome on my Nexus 7 and iPad seems to have some strange desire to provide both mobile and other bookmarks, and wants to display them in a grid. Just weird. Even so, it's nice having my bookmarks on the mobile device. Maybe someday, I'll get my extensions running on my Nexus 7 (hint-hint).
How often used: Constantly.
Live without it factor: It makes Chrome my must-have browser of choice.
I find Buffer to be very helpful in letting me queue up posts for Twitter as I do my morning reading. It used to be that I'd do my daily morning reading, find something tweet-worthy, and post it then and there. That would often mean there were 5-10 tweets posted one after the other, at about 7-8am. Not the optimal tweet time.
Buffer allows me to "buffer" my tweets, grabbing them when I do my morning reading, but sending them out over the day. It's limited to 10 buffered items a day in the free version. A $10/mo "awesome" version will get you unlimited tweets. I haven't yet found a need to send that many daily tweets, so I'm sticking with the free version, for now at least.
How often used: Daily, almost every morning (except weekends, when I let myself off the tweeting hook).
Live without it factor: I could, because my daily "tweeting" activity isn't mission-critical. I'd just go back to spewing all my day's tweets at once. But I think this makes it nicer for everyone.