The web browsers Google Chrome and Mozilla Firefox have long been able to run browser add-ons to extend their functionality and their safety. While there are thousands of add-ons available, there are only a few that are essential for an average user. Many people use ad blockers. One of the most used is AdBlock Plus. Since the company who runs AdBlock Plus decided to allow certain ads, a lot of users switched to the more powerful add-on uBlock Origin. It not only blocks ads but is a universal content blocker meaning it can replace several popular add-ons at once. NoScript for Firefox and ScriptSafe for Chrome are script blockers. They are often recommended for safety and privacy reasons since Javascript and other scripts are not only used to make most good websites function the way they do but also perform malicious attacks on hacked or evil websites. As you can imagine this can result in a lot of work for the user since almost any website uses Javascript these days. uBlock Origin also allows to choose which scripts to block in the advanced settings. If you are unfamiliar, watch my recent video on Advanced Blocking with uBlock Origin. Frankly, it does not offer as many options and features as NoScript but should be all they need for most users. Privacy Badger is an add-on for Chrome and Firefox by the Electronic Frontier Foundation, a respected non-profit digital rights group.
Privacy Badger also blocks content but does not use filter lists unlike most ad blockers. Instead it learns with time which domains seem to track the user and blocks them. This way every Privacy Badger user creates their own custom block list in the background. Unless you don't want to rely on block lists and you are opposed to doing any kind of configuration, ad blockers will give you a very similar result. If you are going to use only one simple add-on, Privacy Badger might be it but in my opinion, it is mostly redundant if you also use a content blocker like uBlock Origin besides it.
One add-on that doesn't block content but makes sure your web browsing is encrypted most of the time and therefore private is HTTPS Everywhere. Basically the add-on checks if the page you are about to visit also offers an encrypted version using HTTPS and if so, redirects you. HTTPS Everywhere is also made by the Electronic Frontier Foundation and is a safe add-on to recommend. There aren't really any popular alternatives and it has little to no drawbacks. HTTPS Everywhere is therefore a good choice to use alongside a content blocker.
Ghostery is another script and content blocker available for Chrome and Firefox. It uses filter lists like other ad blockers but earned a bad reputation for working together with advertising companies and optionally sending data back to the developers. As far as I know, Ghostery uses it's own hidden filter lists which might be more comprehensive than these of other add-ons but in the end it should not make much of a difference. If you have no problem with their business model and don't mind overlapping functionality, try Ghostery. Otherwise stick with another content blocker and HTTPS Everywhere.
Similar is Disconnect, an add-on made by a public-benefit corporation from the United States. It blocks trackers and offers a private search but unless you need their VPN feature or their search, you don't need to combine it with an adblocker since many filter lists from Disconnect are already integrated in other content blockers. They also offer premium service for either a one-time fee or a subscription.
Now one of my new favorite add-ons that isn't strictly mandatory but very helpful: Self-Destructing Cookies. This add-on deletes all cookies once you left a website or after you closed its tab. it's possible to add a whitelist so you don't lose any active logins and can regularly clean the browser cache as well. Unfortunately it is only available for Firefox. A similar add-on for Chrome seems to be Tab Cookies although I have no experience with it. Self-Destructing Cookies makes sure you cannot be tracked by using cookies and therefore cleans up any mistakes other blocking add-ons might have made.
Also only for Firefox is Better Privacy, an add-on for deleting so called super-cookies. These are different than normal cookies since they aren't deleted when clearing the browser history and are usually placed using the Adobe Flash plugin. They are primarily used to track users and any privacy conscious user should want to delete them.
An optional add-on you might want to consider is called Decentraleyes. Lots of websites use Content Delivery Networks (short CDNs) these days to speed up the loading times of their content. But since often thousands of websites use the same hand full of CDNs, it is easy for these networks to track users across different websites. Decentraleyes blocks connections to these CDNs and instead delivers the content locally. The add-on is still in development and only works with selected CDNs. In conclusion my personal recommendation would be uBlock Origin together with HTTPS Everywhere, Self-Destructing Cookies, Better Privacy and Decentraleyes.
I know some of these add-ons are only available for Firefox but let's be real: If you honestly care about your privacy, Google Chrome shouldn't be your first choice of web browser. If you are a die-hard Chrome user, either stick with the add-ons that are available and protect your privacy as well as possible or try Firefox. It's performance has gotten a lot better due to recent optimisations.