Plenty of online games claim to be "casual". You can just log in once per day or so, do your business, and get back the next day, and still be on par with the people who live, eat and breathe the game.
Lies. All lies. And some statistics.
Anything with production caps breaks the casualness. Nile Online caps your wares depending on how much you have upgraded your warehouse - and if you're not overleveling the warehouse, the caps are pretty close to what you need to upgrade your palace (and if you're still following me, upgrading the palace is pretty much the goal of the game). So log in often, or waste production.
Production queues are the other bugbear. Nile Online (again) only lets you upgrade one building at a time, with no queuing. In the early game, upgrade times are between 15 minutes to an hour. Log in, upgrade, log out, wait 15 minutes, upgrade. Better not have a life away from Nile Online. EVE Online players might recognize this pattern to skill upgrades, but EVE is hardly "casual".
Cantr II handles it a lot better. You log on, tell your character to pick weeds, and then he does that until you log on again (or until your inventory is full, but that takes days in Cantr II).
Kingdom of Loathing is also nice like that. You get a bunch of "turns" every day, but they stack so you can get back in everyfew days. Unfortunately, funny games suck, but KoL kept me interested a long time.
Some online games are just way more suited for casual play than others. Random thoughts over.