In 2013, Google added a full-fledged notification center to Chrome for Windows, Mac and Linux that combined rich notifications from web pages with Google Now info. However, it seems that almost no one ever used that notification center, so Google's killing it in the next version of Chrome. In its Chromium blog, Google admitted that "few users" visited the notification area, so it would be removed to streamline the desktop experience.
Notifications will certainly still stick around Chrome -- earlier this year, the browser started supporting a new web standard for push notifications from web sites. But it sounds like there won't be an easy way to see what you might have missed while away from your computer, and it also looks like there won't be any way to get Google Now info on your desktop, either. On ChromeOS, Google recently moved Google Now info out of the notification center and into a new app launcher that combines search, Google Now, and your frequently-used apps. Whether or not there will be a new way for Mac, Windows and Linux users to get to Google Now remains to be seen.