Diablo's storyline: there are devils in crystals. They got out and did bad things. You want to stop them from doing these bad things by re-imprisoning them and/or banishing them back to hell.
...that's about it. I've heard more than a few people talk about how Diablo's story really drew them in/was great/etc., but I've never really understood what they're talking about when there's barely any story in the games. It's hack'n'slash with a goal; it's Gauntlet with voiceovers. Where's the epic story? Seriously, I don't think I've had someone give me an example yet.
Starcraft did have one major high point in the story: New Gettysburg. The rest seemed...well, for lack of a better word, "standard" to me. Cowboy forced to deal with scumbags for the greater good, can't stand the man when he goes too far, sides with the noble demons and finds out they're Not So Different when it comes to core values in some ways. The woman scorned comes back with a vengeance. Heroic sacrifices ensue. It had twists and turns but they all had clearly-marked Detour signs before they arrived.
Starcraft 2's storyline suffers from choose-your-path syndrome: it's hard to make a coherent and complex story work if various pieces of it can come at different times. I imagine if they'd had all 20-something missions in a linear order they'd have made a more sensible plot throughout, but when you can out the Korhal empire's evils early on and then backtrack to save idealistic colonists afterward or save the colonists and do some covert ops before you ever bother downing the empire, you can't really expect the pieces to fit together very neatly. Fun mechanics, not so good for story.
I know I'm more critical of writing than almost any aspect of a game - it's what I know best - but even so, Blizzard games have never so much as been on my radar as examples of great storytelling. They do a passable job, but that's about it; the gameplay overshadows the writing every time.
Not really sure how to address the cookie-cutter comment as I'm unsure what you think their cookies are cut from. If you mean they're cookie-cutters of their own games, Diablo 2 is pretty distinct from Diablo as far as character customization and abilities go, and Starcraft 2's gameplay is significantly varied from Starcraft - the mass uproar from fans about various parts of the original game that were removed or exaggerated or dumbed down or changed at all seems like a pretty good indicator of that even if I didn't notice it in my own play. The core's the same - it's an RTS with the same mineral/gas baseline economy - but the layers added onto it have definitive variance. Watching some pro games of Starcraft and then a few of Starcraft 2 makes the differences in strategy more readily apparent.
If you meant they're cookie-cutter versions of other games...which ones?
@Inkidu: I'm still not sure what to think of releasing SC2 in race-based installments, to be honest. From a payment standpoint I can't say I like it 'cause, well, it means paying more to get the other campaigns, which obviously isn't cool for me. From the standpoint of actually playing the game, I dunno, it's about as much content as the initial Starcraft's 3 campaigns put together with a lot of extras on top, so it's not like I feel robbed by getting just the Terran campaign alone. Call me Undecided-Frowny on the subject for now, I guess. At least they didn't end the story on a cliffhanger; you could take it as the end of the story if you wanted, though for anyone who's been playing from the first game it's unlikely to feel complete there.