1-Click Timer - I am definitely guilty of setting time guidelines for students and then getting distracted. This is a quick timer I use all the time to help keep the classroom on track. I like that it is quick to set and unobtrusive - you can see how many minutes are left just by looking at the icon in your toolbar.
AdBlock - I use this at home and work, and it is hard to think of life without it at this point. I know I've had times when I've tried to show students websites, only for an inappropriate banner or pop-up ad to show up. With AdBlock, when you see something that you don't want to see, be it a picture of a spider or a flashing banner ad, you can right click and block it.
Adblock for Youtube - Along those same lines, I don't want to see a car advertisement blaring before I show a clip to students. This extension cleans the ads up for you automtically.
CraftyText - When you need to show a join code or a short URL to the whole class, just copy/paste it into CraftyText and it will display the text large and centered across your screen for projection. This saves the time you normally spend zooming in and out or repeating yourself endlessly.
Clean Print - If you have articles that you want to print for students, or just make a PDF of, I really like this extension because it removes the banners and extraneous things so that you can print as few pages as possible. You can also manipulate the page before it gets printed or turned into a PDF in case there are things that Clean Print hasn't automatically removed that you don't need.
DocHub - I used this extensively to help get scanned documents rearranged the way I want them to be and fill out PDFs/create PDFs that others can fill out. And it is all FREE!
Read & Write for Google - This is an extension I had every single student add. It is an amazing tool for checking fluency, not to mention a great help for differentiation for struggling readers on any website.
Strict Workflow - I use this personally, but I can see it working well for students who need a visual reminder of how long they should be on task before taking a break. As a teacher, I know I get distracted when grading and wander off on the internet. This extension actually allows you to set particular websites that are banned while the timer is on, and they are all unlocked for a break. You can also adjust the timers to suit your needs. I both love and hate this extension, depending on whether or not I am trying to actively grade essays.
TabCloud - When I am working on paperless grading, I usually have a series of tabs that I like opened up in a certain order. With TabCloud, you can save whatever tabs you have open and then reopen all of the tabs with one click at any time. My workflow goes so much faster when I can just open a new window, click TabCloud, and immediately get everything open that I need to grade.
TabScissors - Another extension that I've had all of my students add. When you click on the icon, this splits the window at whatever tab is currently active, giving you side by side windows of equal proportions. Note - this only splits half of the tab correctly on Chromebooks for some reason, but then students usually figure out resizing the second window so that they can have text open while filling out a Google Form, for example.
Visor - I can see this being useful for both teachers and students. What it does is allows you to adjust the contrast of your tab or dim it to make it easier to read, but most importantly, allows you to highlight one line at a time (following your mouse) to help you and struggling readers focus on the text. I've used this when cross-referencing a long list with tiny print for yearbook orders along with helping me read when my attention is elsewhere.