You can check for suspicious log-ins and password changes.
Ed Rhee, a freelance writer based in the San Francisco Bay Area, is an IT veteran turned stay-at-home-dad of two girls. He focuses on Android devices and applications while maintaining a review blog at techdadreview.com.
Your Google account is responsible for giving you access to more than just your e-mail nowadays. Your Google account provides you with access to a wide range of Google services, including Google Music, Google Drive, and Google+. It also allows you to log in and set up devices, like Android smartphones, tablets, and Chromebooks.
To help you keep an eye on your Google account, Google tracks your recent account activity and allows you to review them from your Google Dashboard. It's similar to the Gmail "Last account activity," but includes more than just your Gmail activities. To view your recent Google account activity, click on your Google profile photo, then click Account. In the left column, click on Security, then Recent Activity. You can also go directly to https://security.google.com/settings/security/activity.
Most of the items are log-in activities, but you'll also see some password and recovery activities as well. For log-ins, you can see from where the log-in originated, the browser used, operating system, and IP address. Keep in mind that the activity list, as Ghacks notes, is for Web log-ins only.