In Tools > Options > C/C++ > Other, there is no option for C++17 as the default standard.
How do you compile code that requires C++17?
Updated 3/28/21 for NetBeans 12, as documented at the end of this answer.
The C++17 standard was published over a year after NetBeans 8.2 was released, so C++17 is not available as an option in the standard release of 8.2.
However, NetBeans Bug Report Bug 271136 - Support C++17 standard addressed this deficiency, and if you download and install any of the most recent nightly builds of NetBeans 8.2 from 2018 the issue is resolved; C++17 is available as an option when creating a C++ project:

If you then select {project} > Properties > Build > C++ Compiler you can verify that the C++17 standard is being used:

Notes:
- When you create subsequent C++ projects, the project wizard will continue to use the C++17 standard by default, so it becomes "the default standard" unless/until you select an alternative.
- Using a nightly build of NetBeans 8.2 instead of the standard release is also preferable because it contains many unrelated bug fixes.
- An even better alternative (if it is possible for you) is to download and install the latest release of NetBeans, Apache NetBeans 11.2 which also provides C++17 as an option.
- If you install a nightly build of NetBeans 8.2, or NetBeans 11.2, your existing installation of NetBeans 8.x will not be touched, so you can safely revert if necessary.
Updated 1/21/20 and 1/22/20:
These are the steps needed to make C++17 available on NetBeans 11.2:
- Opening the project wizard using File > New Project... shows that C/C++ projects cannot be created by default.
- Select Tools > Plugins > Settings then click the Add button.
- In the Update Customizer Center screen, set Name to NBDevDarkThemes and URL to http://bits.netbeans.org/dev/nbms-and-javadoc/lastSuccessfulBuild/artifact/nbbuild/nbms/updates.xml.gz and click OK.
- Ensure that only the entry for NbDevDarkBeans on the Settings tab is checked.
- Install the C/C++ plugin by clicking the Available Plugins tab, then checking the entry for C/C++. The version for that plugin should be 1.31.5.1. Click the Install button.
- After the plugin has been installed, click the Installed Plugins tab, check the Show Details checkbox and scroll down to verify that the C/C++ plugin is installed and Active:

- Go to Tools > Options > C/C++ >, click the Build Tools tab and configure your external C/C++ environment as required. For example:

- Now go to File > New Project... and you should be able to select C/C++ > C/C++ Application.
- Click Next >. On the Project Name and Location screen you should now be able to select C++17 for the standard:

Updated 3/28/21 for NetBeans releases 12.x:
Bad news: NetBeans no longer officially supports C++! See the definitive response from Geertjan Welenga, leader of the NetBeans Team, dated 3/25/21 in response to the recent bug report NETBEANS-5501 C++17 no longer available:
*At the moment, NetBeans doesn't support C/C++, the plugins you were/are using from 8.2 are not really officially supported, though work on this is ongoing here, with an end goal to having it officially part of NetBeans, though that will take a while:
https://lists.apache.org/thread.html/r4ac84633554ce80d99b0710e7a803ce1dc322680c914b18058876b51%40%3Cdev.netbeans.apache.org%3E
You're welcome to join in with the discussions on dev above.*
That said, there is an unofficial workaround, as detailed in bug report NETBEANS-4452 The Plugin Installer found problem timeout of loading C/C++ Remote Development API... while install the following plugins: C++. That is:
- Download JDK 8 (if necessary).
- Temporarily set the JDK NetBeans 12 uses to JDK 8 by editing netbeans.conf, then restart NetBeans.
- Install the relevant C/C++ plugins.
- Reset the JDK NetBeans 12 uses to the one you were using originally - presumably to JDK 14 for most users - by editing netbeans.conf, then restarting NetBeans.
- C++ 17 should then be available on NetBeans 12, on the clear understanding that it is not officially supported.