For Chromebook users, Google offers Guest Browsing option which is similar to Incognito mode, doesn’t saves browsing history when you close all open Guest windows, however all the files you downloaded will be preserved. Guest Browsing is enabled by default in Chromebook, if you’re interested, you can try the same in the Chrome browser, for that, you needed to be using Canary or a developer build.
Note: Check the update below.
Turn on Chromebook’s Guest Browsing in Google Chrome
To test/enable Guest Browsing in Chrome
1. Visit Chrome://flags in the browser address bar and enable the below two flags
Enable new profile management system, and Enable GAIA profile name and icon.
2. Restart the browser.
3. Now profile switcher appears in upper left-corner of Chrome, click on it and further click on Guest browsing, which then opens a Guest Browsing window and shows the message you’re browsing as Guest.
With Guest Browsing, Pages you view in this window won’t appear in the browser history and they won’t leave other traces, like cookies, on the computer after you close all open Guest windows. Any files you download will be preserved, however.
To exit from it, you can simply use the keyboard shortcut Ctrl +Shift+Q or click on Sign out by clicking on the Profile Switcher.
Update December 24, 2014: you no longer need this as Google has added new user menu to switch users and access the guest mode aka guest browsing mode.
To access the Guest browsing mode, click on user icon > Switch Person > Click on ‘Browse as Guest’ (check the screenshot below).