Honestly, I feel like nothing will top the old MSN/Windows Live Messenger days for me. Not even Discord captures that same feeling. Of course, that could be nostalgia itself talking, but being randomly invited to a group chat by one of your friends and messing around and having crazy usernames was one of the most memorable parts about it.
Also, nudges. Not that I'm the annoying type that does them, but nudges were hella funny. :x
Oh, and AIM! Now I wasn't a huge user of AIM, but it was certainly interesting to use for the like...2 or 3 people I had on my AIM list , lol. I will never forget how using it made me feel like MSN was a more "modern" (at the time, anyway), way of chatting.
And I dunno if they're still up these days, but I miss the third party sites that allowed you to sign into IM services like MSN, because I used the crap out of them when I was somewhere like school where I couldn't download MSN but I still wanted to talk to my friends. Fun stuff.
Last thing, IRC. I know IRC still "exists" (probably), but for the most part it's largely a wasteland and I really miss the days where I would download the mIRC client alongside NNS (NoNameScript was especially super cool because it allowed you to customize the look and feel of your client to make it look significantly less ugly than what the mIRC client was) and just hop on various IRC servers and start chatting. Really, IRC, alongside MSN was how I've made some pretty crazy memories with some people because I remember we used to have clique channels and those were nuts, haha.
The internet sure was a hell of a place in the mid-late 2000s.