CentOS 7 - end of life in 2024, then what

If RHEL binary compatibility is not strictly required and if using in-tree kernel modules only (i.e.: no out-of-tree kmods are required), CentOS Stream should remain a viable option.

Otherwise you can use one of the new RHEL clones, such as AlmaLinux, RockyLinux or even Oracle Unbreakable Linux (in this case, be sure to select the RHEL-compatible kernel rather than its own customized kernel). Personal note: I am using RockyLinux with no issues at all (I migrated from a CentOS 8 box with the migrate2rocky script) but, as always, your mileage may vary.

Finally, if you are sure to need fewer than 16 RHEL instances, you can use plain simple Red Hat Enterprise Linux from Red Hat's free tier (with no support, obviously).

EDIT: as wisely suggested in other answers, migrating to a different distributions as Debian, Ubuntu, etc. is a very reasonable approach. I did the same (rebuilding with latest Ubuntu LTS) in environments where RHEL compatibility was not required. Debian and Ubuntu officially support in-place upgrade paths while most RHEL clones only have unofficial support - RHEL itself and Oracle Unbreakable Linux being the exceptions, with fully supported leapp upgrades - but things are changing now.

This answer is biased - I'm working for a company making an RHEL clone.

You have multiple options:

• Migrate to stable platforms with a good history like Debian and Ubuntu. Ubuntu actually became even more popular last year when it comes to enterprise market. They made a huuuuge pivot.
• Migrate to SUSE Linux - they have a very similar business model to RHEL. Unfortunately, there is no free clone of SLES. EDIT: There is SUSE Leap that aims to be binary compatible with SLES - see @sebix comment.
• Migrate to one of the new RHEL clones. The ones with the most traction are AlmaLinux and Rocky Linux. In my opinion Alma is a much better choice. The organization is Non-Profit, CloudLinux OS that started it has a good history with the Linux community - still the project is run mainly by a professional company. In the meantime, Rocky Linux was created by the CentOS founder. The company is For Profit, Public Benefit Corp and is started/backed by CIQ that was/is a company owned by the very same person.
• Migrate to the RHEL clones with a bit longer history. Here you have Oracle Linux that, IMO in many cases, is phenomenal. The only problem with Oracle Linux is, well Oracle... The other choice that I can propose is EuroLinux (the company I'm working for). We are honest - it's open core model (everything is free to use. One can pay for support or create your own local RHEL clone with our build system). We are better in multiple places, and in some we are worse (for example, our community is tiny).
• The last options are enterprise Linuxes that are the closest to the thing that CentOS was. Here goes Springdale Linux. Princeton University runs it, so they and AlmaLinux are the ones that are truly not profit/community-based.

Lastly, if I could recommend something - don't jump the gun - you will have enough time to see which project will be the next stable CentOS replacement, in the case of the enterprise Linuxes it is not a sprint but a marathon.

I had to get our system off CentOS6 (we'd been slacking) when the news about 8 hit. Ultimately I wound up moving us off of DevOps and CentOS to Ubuntu 20.04 (LTS release).

I realize that it's not a 1:1 move, but we were largely using web servers and most of our setup could be replicated in Ubuntu. The pain points were

1. Switching users. CentOS uses httpd for the user, while Ubuntu uses www-data (running them in a hybrid config was a pain)
2. Services were named differently as well. PHP processes are no longer php-fpm, but phpX.X-fpm. Apache is not httpd but apache2
3. Finding new repo sources for some packages. We run a later version of PHP than the LTS versions offer

The advantage is that Ubuntu's community is much broader and better supported. It was worth the hassle in the end to just up and ditch CentOS.

Simply as another datum, this issue has been the impetus I needed to decide to end twenty-some years of using RH/CentOS for production deployments (I think I started with Red Hat 4.1). All my new deployments are Debian (unless clients specifically request C7 and indicate their understanding that we'll be back for another rebuild in 24 months) and I'm in the slow process of migrating all my existing deployments. Whatever else Debian does, it's very unlikely to make my life difficult the way RH recently has, and any other corporately-driven project could equally do at the drop of a CEO's hat.

All my C6 systems had to be rebuilt in order to get to C7, so the idea of one last rebuild in order to get off that cycle, to a distro that regards in-place major version upgrades as a normal activity, seems worthwhile.

I've already discovered some issues, and I've no doubt I'll find more, but I'm six months down that path, and have not yet found a reason to turn around.

For CentOS 7, I suggest CloudLinux 7 — I guess they will do the same as they did for CentOS 6?

A replacement for CentOS 8 is Alma Linux.

One suggestion that hasn't been covered is bringing your infrastructure to Red Hat. Red Hat has tools like Insights, Performance Co-Pilot, and Identity Management built into the operating system. You can have access to our support engineers and work with Red Hat to influence the future of the upstream projects you depend upon.

As one commenter mentioned, if your need is less than 16 nodes, you can migrate to RHEL for free. If you have a need for a larger infrastructure, we also have developer licenses so your Dev/QA environments can be running the same OS as the paid-for production licenses.

Red Hat has also made it easy to migrate from CentOS7 to RHEL7 with Convert2RHEL and from RHEL7 to RHEL8 with the Leapp in-place upgrade tool!

(Disclaimer - I work for the Red Hat Enterprise Linux team, however, this would be my recommendation regardless.)