Incognito mode can help keep your browsing private from other users, but it can't keep your browsing activities private from your ISP or online snoops. For that level of privacy, you'll need to connect to a virtual private network (VPN).
All incognito mode will do is erase your browsing and search histories while in private mode, as well as dump any tracking cookies you pick-up during your incognito session. If you're unsure how to turn on your browser's added privacy mode you can find instructions online for Chrome, Firefox, and Internet Explorer.
Outsmarting leaky paywalls
Several websites put the majority of their content behind paywalls, but allow you to view a limited number of articles for free per month before forcing you to pay for a site subscription. These paywalls are designed with many ways around that 10-article limit, however. Sites such as The New York Times will let you continue reading an article for free if you follow a link from social media like Facebook or Twitter even after you hit your limit.
Another option is to just open your browser in incognito mode. This way, no cookies are kept on your PC and every time you visit a leaky paywall site it's like you're a new visitor with a fresh 10-article limit. Clever, clever.
Private accounts, public PC
Public locations often have PCs that are often poorly maintained and may not erase your browsing history after your session.
To make sure nobody stumbles across the login page for your personal website or any other sensitive account, just use incognito mode on public PCs. It's not a bullet proof form of protection, but combined with telling sites not to store your password and using a dash of common sense, incognito mode becomes an effective form of protection.
No history, please
Perhaps you want to get information about a medical condition, and you'd rather not have the search terms pop up later on the family PC. Or maybe you're shopping for a surprise gift and you don't want anyone to see what you were up to at Amazon or Overstock. Really, the reasons for keeping some portions of your browsing history private are endless. Your browser's private mode keeps your browsing, well, private.