Mailing lists, which were sometimes called "reflectors" in their early days, are one of the older pieces of Internet technology. Despite that, they're still heavily used -- including by the very people who built and still run the Internet, people who could use anything they wanted. The Internet Enginering Task Force, the World Wide Web Consortium, the North American Network Operator's Group, and many more all do their work via mailing lists.
That's not an accident. It's because mailing lists have enormous technical advantages over the alternatives. Here are some of those:
1. They're asynchronous: you don't have to interact in real time. You can download messages when connected to the Internet, then read them and compose responses when offline.
2. They work reasonably well even in the presence of multiple outages and severe congestion.
3. They're push, not pull, so new content just shows up. Web forums require that you go fishing for it.
4. They scale beautifully.
5. They allow you to use *your* software with the user interface of *your* choosing rather than being compelled to learn 687 different web forums with 687 different user interfaces, all of which range from "merely bad" to "hideously bad".
6. You can archive them locally...
7. ...which means you can search them locally with the software of *your* choice. Including when you're offline. And provided you make backups, you'll always have an archive -- even if the original goes away.
8. They're portable: lists can be rehosted relatively easily.
9. (When properly run) they're relatively free of abuse vectors.
10. They're low-bandwidth, which is especially important at a point in time when many people are interacting via metered services that charge by the byte and are WAY overpriced, and getting more overpriced every day. This will get worse, not better, with telecom industry consolidation and deregulation.
11. They impose minimal security risk.
12. They impose minimal privacy risk.
13. They can be freely interconverted -- that is, you can move a list hosted by A using software B on operating system C to host X using software Y on operating system Z.
14. They're archivable in a format that is likely to be readable long into the future.
15. They can be written to media and read from it. This is a very non-trivial task with web forums: just try doing the equivalent of #13 above. Good luck with that.
16. They handle threading well. And provided users take a few seconds to edit properly, they handle quoting well.
17. Numerous tools exist for handling mbox format: for example, "grepmail" is a highly useful basic search tool. Most search engines include parsers for email, and the task of ingesting mail archives into search engines is very well understood. Excellent archiving tools exist as well.
18. The computing resources require to support them are minimal -- CPU, memory, disk, bandwidth, etc.
19. Mailing lists interoperate. I can easily forward a message from this list to another one. Or to a person. I can send a message to multiple lists. I can forward a message from a person to this list. And so on. Try doing this with web forum software A on host B with destinations web forum software X and Y on hosts X1 and Y1. Good luck with that.
20. Mailing lists can be uni- or bidirectionally gatewayed to Usenet. (The main Python language mailing list is an example of this.) This can be highly useful.
There's more, but I think this easily suffices to make a slamdunk case.
Frank Zappa once said that you can't be a real country unless you have a beer and an airline. I don't think you can take an organization or a project seriously unless it has a mailing list and/or a newsgroup.
Of course there's always a temptation to rush to the latest greatest shiny thing (e.g., Slack appears to be popular right now) because it's new and shiny, but those come and go, and they depend on the vagaries of the companies behind them. Many painful object lessons in the impermanence of such things may be found at http://archiveteam.org -- whose contributors have invested heavily in attempts to mitigate the consequences of ill-advised decision-making by others.
Not to mention that many of those latest greatest shiny new things come equipped with hideous privacy and security issues that can't be fixed because they're fundamental parts of the design. Not that mailing lists are immune to these -- they're not -- but the privacy and security exposure is far less.