In my opinion, one of the best things about Google's Chrome browser is the excellent selection of browser extensions. In the past, Firefox has taken the title for largest selection of extensions, but recently I'm seeing more and more really good Chrome extensions. Since two of these extensions are available for Firefox as well, I'll give you links for those versions too.
Here are five of my favorite extensions.
1: AutoPager (Chrome and Firefox)
Have a favorite site that likes to split articles over five different pages, requiring you to click the Next link every time you get to the bottom of the (usually about two paragraphs long) page? AutoPager automatically loads the next page once you begin to reach the bottom of the page you're currently on, then tacks it onto the end of the page you have.
It does require a "rule" for each page, but most popular sites have rules uploaded by users, and if you really want it to work with a site that doesn't have a rule, you can always write one yourself.
2: Better Omnibox (Chrome only)
The "omnibox" is the improved address bar in Chrome that can be used to load websites by typing just the first couple of letters, search the web, and search websites (type the first couple of letters of the site you want to search, then press Tab). Better Omnibox extends this to allow you to search your history and bookmarks as well by simply pressing #, then entering your search terms. Searching history and/or bookmarks always used to be a painful process, requiring opening up the history page or bookmarks manager, and it never seemed to work quite right for me. With this extension, finding a page I visited yesterday is as easy as it could possibly be.
3: Chrome Remote Desktop (Beta) (Chrome only, obviously)
This extension is just what it sounds like--you can access another computer remotely. You need a person sitting at the computer you want to access, who clicks the Share button and receives a code and sends it to you; you simply type the code in and are on your way.
As a makeshift tech support representative for quite a few people, this extension comes in handy occasionally. Trying to write a script for somebody over the phone (or worse, Facebook chat with a slow typist, as it was last time this happened) is more frustrating than you can possibly believe until you've tried it. After I finally thought about this extension, the problem was fixed in under five minutes.
Also nice is the fact that this extension is completely cross-platform: you can access a Mac from a Windows PC, a Linux PC from a Mac, or even a Windows PC from a Chromebook. It's supposedly still in beta, but I've never had a problem with it.
4: Visual Hashing (Chrome and Firefox)
This handy extension changes the white background of password fields to four colored bars which change as you type your password. Each set of colors is the result of a mathematical calculation based on the password you type, but there is no way to derive the password from the bars, so this won't help anyone watching you figure out your password. On the other hand, once you've typed your password and watched the pretty colors a few times, you'll notice that the colors don't look right and realize you've mistyped it before you hit Enter and wait fifteen seconds for the site to reload and make you type everything in again.
5: Chrome Daltonize (Chrome and sort of Firefox)
This extension is a bit more obscure, but it's still interesting. Its purpose is to filter the colors in images that appear in web pages. It can either simulate colorblindness or perform the Daltonization technique, which creates more contrast and makes it easier for people who are colorblind to differentiate the colors in the image. This extension is probably a bit more useful for me, since I actually am colorblind and occasionally have difficulty with fancy graphs and maps on the Internet, but most of the people with normal color vision to whom I've showed the simulation have thought it was pretty cool too, so it might be fun to play with anyway.
Once you've installed the extension, right-click on the little color wheel that appears on the toolbar and choose Options. Chances are fairly good the default settings aren't what you want. You can either choose to Daltonize or Simulate any of the three main types of colorblindness; if you actually are colorblind, you probably want to choose the one that corresponds to the type you have. (If you're not sure, check out the handy test at http://www.colour-blindness.com/colour-blindness-tests/colour-arrangement-test/
.) If you're just playing around, you might want to try each of the settings in turn.
Once you're done with the settings, close the tab, browse to the page you want to try the extension on, and click the color wheel button.
There is no native Firefox extension, but there are bookmarklets available at the download link. To use a bookmarklet, just drag the link to your bookmarks toolbar or menu, browse to the site you want to use it on, and click it. (It might take a second to work; be patient.) With the bookmarklets, you need to drag a different link depending on which settings you want; see the Chrome configuration section if you're confused about what they are.