There was someone that mentioned they liked incrementals/idle games a while back, so I've finally found one I like. Kind of. I still dislike the genre at large, but this one contains lots that I do like, so I'll give it a mention.
Clickpocalypse II is a Diablo themed incremental where you make a party of four characters and they roam about the countryside clearing monster infestations from dungeons. And attacking castles. Because apparently there's an endless winter happening and it's the monsters' and castle owner's fault. Probably.
Things I like about the "game": It's got a graphical representation of your party running around dungeons killing stuff. Your party selection does change how they kill stuff. You get to pick skills at level-ups, which can make your party kill stuff in different ways. There's no sound, so it's relaxingly non-repetitive. There's potions and scrolls to use, so there's stuff to click on while you're watching. The offline background mode lasts a while (3hrs), which can be boosted, so you can just load it up to collect your stuff, level-up your characters and watch it for a few minutes if you want.
Like most incrementals, you can't actually die, so it's just a matter of making the big numbers bigger. There's an actual end-point in the "game" (are incrementals really games?), so you can try out something different and see if it's faster next time. There's character unlocks and permanent bonuses to get as well.
So far I like it, as this sort of "game" goes. Some stuff is weird and I don't know what's actually efficient. Like my party of 2 priests and 2 druids looks nice, but they kill slowly. But the druids have great stats, so probably kill pretty quickly in offline mode. And I've kinda backed myself into a corner with the priests if double group-buffs don't stack, and if they're not used as stat-boosts in offline mode. I'm not sure if the druid's slow spell (essentially a web scroll) actually makes things slower to kill in online mode either. It often seems that way. Whatever.
Oh, and online means actually playing/watching, and offline means not doing that. It doesn't need an internet connection or anything.
Anyway, if you like incrementals, give it a go. The diablo-esque presentation and RPG'ness of it is kinda cool. And there's at least some player choice in the matter of party makeup and levelling order (as well as setting up potion bursts for xp/gold when actually "playing"). I hate incrementals, but if I'm going to have one on my phone, it's going to be this one.