Agree with all the above so far - as @Hawk says, notifications are mega important and I know a lot of people rely on them for keeping up to date with things. similarly being able to send/receive summary/digests of what's been going on at a frequency that works for you is also important. Ties in a little with @Travis newsletter thoughts too.
Another thing for me that is so important is the ability to @mention someone - it's an assumption I make that the leading, if not all, community platform vendors do have but without it life would become more difficult to pull people in to conversations that a) they can add value to and b) get value from.
And finally (for now) the ability to Direct Message people privately is also pretty essential. I use it in my own community to reach out to Community users and build a relationship with them there, get to know them a bit better, and be able to understand what might help them become more engaged, what topics might interest them, what value they're looking for, but also just from a relationship perspective - it just helps engagement when you like people you're engaging with.
If I think of others I'll come back to this one for sure.
And thanks @HAWK for using the feature you mentioned for inviting me to the convo!