What you 'muricans can expect:
I'm on a "high" pop realm, but not one of the really overcrowded ones. Like well outside the top 10, probably more like the 15-20th most populated or something thereabouts.
Two hours before launch, the server started crashing every couple of minutes. While they claim to have some sort of sharding of the Blasted Lands zone, there were still hundreds if not thousands of players standing on top of the NPC. It took 10+ minutes for it to load and another 10 minutes to respond to clicking the quest acceptance thing. With the server crashing every few minutes and the world server being down half the time, it was an hour and a half beyond midnight before I could even get Khadgar to appear and give me the quest.
The phased introduction was fine, but as soon as I entered Shadowmoon Valley, it wasutterlyunplayable for the next 2-3 hours. We're talking delays of up to a minute on all actions and events. It was virtually impossible to kill anything as combat was so delayed that you had no idea what was going on and mobs wouldn't load in until long after arrival/respawn. Fortunately I'm a balance druid so I can just cast Starfall and it'll take care of shit, but most other classes were completely incapable of killing anything. While it doesn't show on the latency thingy, I'd say we had about 30-50,000 latency. Sometimes it took several minutes to loot a corpse.
Once the lag settled somewhat around 3-4AM, it became technically playable, though still quite rough--the latency meter didn't indicate any lag, but it felt like ~500ms. However, they must have fucked something up with the quests. Things aren't respawning faster than their standard timers, so you have hundreds of people camping the same half dozen mobs that take two minutes to respawn. It takes at least 10-15 minutes to do any kill quest. Clickable objects are only slightly better, and the fact that their spawns are static means each spawn has a crowd of 30+ people standing directly on top of it. As of 6AM, having barely left the computer since release, I was still level 91 despite going as fast as it was possible under these circumstances. Instances give almost no exp, so while they're lag-free, they're pretty pointless to do as the drops are also worthless to anyone who has SoO LFR gear or better.
All in all, a rather disastrous launch given the game is 10 years old and the last three expansions had a much smoother day 1. I don't know what it is that makes Blizzard stick with completely broken shit like shared quest interactibles, mob tagging and such weak phasing/sharding. Whatever technology they use to distribute players onto different instances of a zone, it still puts thousands in the same one and renders it largely unplayable.
Is there some logistical reason why they can't have all mobs behave like rares, i.e. everyone who deals damage gets quest credit and loot? Is there some reason they can't make clickable shit on the ground phased to the individual instead of shared so that only one player can use them every 20 seconds or whatever? I don't get it. The solutions are so obvious and it's frankly pathetic for these problems to be in a 2014 release by the very biggest MMORPG company in the industry. And didn't previous expansions have mobs respawn faster if more people were around?