Since you ask about Diablo, I'm assuming you ask for something similar to the first game, not the second. If so,
Depths of Peril is pretty cool, with many randomly generated elements. Some quests have a timer and you'll often be forced to chose between doing one or the other but not both, some quests even involve the town and if you fail them, a shopkeeper can be taken out for the game for a while, effectively closing his inventory with you, and there is the matter of having other computer controlled opponents trying to solve the quests before you. That said the diplomatic part can become a bit easier once you figure it out, and is certainly exploitable, but the game still packs a lot for the price. They have a demo that should give you a good idea of how the final game is, so you can give it a spin. If you like it, you can buy it off their site and download it right away.
Divine Divinity is a good game but a bit different from Diablo because only the loot is randomized, while Diablo offered a completely different adventure each time, with quests, monsters and level layout being picked up at game start. Instead DD gives you a really big world to explore, lots of quests to solve, sometimes in different ways, and a lot of things to fight. The main story is a bit of the standard generic fantasy fare, with your character being the Chosen One who must banish The Ancient Evil back to the hell hole it crawled from, but the side-quests offer a lot more variety and depth, especially those that dabble into politics, and often fall into self-derisive satire. Some places also turns some fantasy clichés upside down, like the village of dwarves who prefer to live on the ground than under it. It also has some lovely ways to let you interact with your environment, sometimes giving you unexpected ways to solve problems: for instance you can pick everything up that isn't nailed down, though most of that stuff is useless for you, but it also means you can pick up treasure chests if you can't open them yet, assuming you are strong enough; you can then drop them in town and go back to them later when you have a higher lockpicking skill. DD has some rough edges, some parts are better than other — the starting and ending sections aren't very good but the huge middle of the game shines — some skills are too overpowered for their own good and can turn the game into a walk in the park if you pick them up, and the main story is of the boring variety, but it thankfully have more to offer. But if you want it, you'll have to hunt for bargain stores, or maybe sail the seven seas.
It also had a spin-off, Beyond Divinity, that I advise you not to mess with. And the sequel, Divinity 2, is in the works.
Ois: Dungeon Siege is also close, but mostly automated in play.
It's so automatic it felt like a screensaver.
Roguelikes are also an interesting choice but they aren't for everyone. Action-RPG like Diablo and roguelikes like
NetHack often gravitate around dungeon-crawling but do it in different ways, with roguelikes often focusing on careful exploration, interaction with the environment and of course planning of your next action. You can try NetHack, it's my favourite of the bunch, but be aware that you'll need to at least read the guidebook that comes with it, because it's not a game that you can simply jump into and start to play. But it's free and has excellent gameplay.
Edit: just read you do not like roguelikes, so forget about this last section.
