Warcraft 3, Age Series (AoE, AoE2, AoM, AoE3), Need For Speed Most Wanted (2005)
I played the first age of empires when I was 6 or 7 y/o and I've played all of the games besides AoE4 (including Star Wars Galactic Battlegrounds).
As a kid we had few crappy dell computers connected to just a hub (LAN without internet) and would play a lot of Age of Empires 2 and C&C Red Alert 1 & 2 multiplayer.
Age of Empires and Red Alert were also games I would frequently play at small LAN parties (although everyone was really bad)
I played a bit of online AoE2 when AoE2 HD came out on steam but it was pretty bad so I stopped playing it. When DE came out I started watching AoE2 content but I'll never play it because I've come to greatly dislike Microsoft over the years.
I've replayed Need for Speed Most Wanted (and also Carbon) tens of times over the years, and I still play it every now and then (with mods now)
But the game I've played the most is probably Warcraft 3. I've played a ton of custom games on Battle.net (RIP) and it's what got me a bit into programming since I liked making custom maps and making triggers eventually led me to learn JASS (Just Another Scripting Language)
If Blizzard didn't completely ruin Warcraft 3 with WC3 ~~Reforged~~ Refunded I'd probably still be playing it and making custom maps every so often.
I have played a bit on private servers but it's just not the same anymore.
There's a pretty cool Warcraft 3 open source project called Warsmash though so maybe one day I'll start playing again.
Warcraft 3 itself never had rejoin as in you could not close WC3 start it up again login and rejoin, but if you were having connection issues it would pause the game and wait a minute or so to give you a chance to reconnect before dropping you.
Some private WC3 servers did a have better reconnection features added, like ENTConnect, but obviously those were obviously just for games hosted by their own bots (although you could still join these games from official battle.net lobby search until Blizzard nuked host botting a year or so before Reforged came out)
But if you get Desynced there's no waiting for reconnection, you're just dropped.
Because being Desynced means the game state on your client doesn't match with the rest of the players, so to fix that the game would have to be rewinded until before the desync happened and no such feature existed in WC3.
And the patches leading up to reforged and Reforged itself added a ton of desync issues.
LAN doesn't exist. Ranked Ladder & profiles didn't exist until 2022, and it still sucks and everyone uses W3Champions instead anyway, and the auto hosted in game tournaments don't exist.
Regarding custom games, the custom games are not made by Blizzard, they're made by players. However in the patches leading up to Reforged Blizzard did add a lot of new functions that modders/map makers could use which were great additions, thus allowing for new cool stuff in custom games.
One super obvious and huge change was that in version 1.30 24 player support was added, instead of the usual 12.
But that doesn't change that Blizzard then also made changes in Reforged that broke basically every existing custom map and they had to be updated to fix.
There were some desync issues and saving games in single player was broken but for custom games version 1.31.1 (the last patch before Reforged) was the best patch, you had all the new functionality added to the map editor but a lot less bugs and problems from Reforged.
Also there still haven't even added the ability to play custom campaigns to Reforged lol. The few single player campaigns you can play in Reforged are thanks to people independent of Blizzard coming up with a work around and they're technically just a series of custom games you play (although that is what campaigns are so).