Okay, time for unpopular opinion time:
-Pre-Diablo I: There isn't really anything to talk about. Warcraft II, maybe, but even then I can't say the cinematics do anything special, Maybe when Khadgar destroys the Dark Portal, but that's about it.
-Diablo I: Cinematic intro. Not my favorite, but still foreboding. Sets the atmosphere well.
-StarCraft I: This is where cinematics start to shine. I'll give shoutouts to Mengsk's speech, Tassadar's sacrifice, the UED victory report, Kerrigan's monologue, and the Amerigo battle. If SC1 has a weakness, it's that a lot of the cinematics feel superfluous. This is partly due to how the game was developed, considering that many cinematics were developed before the story was solidified, so they have to be slotted in at times. Apart from the Amerigo, they exist outside the plot. I feel that as far as cinematic integration goes, CNC 1 & 2 did a better job, even if SC1 had better individual ones (see above).
-Diablo II: Okay, I've said it before and I'll say it again - I don't like Diablo II. I consider it a "good" game, but it's a game that doesn't appeal to me unlike D1 or D3, and the cinematics are part of the reason. Taken by themselves, they're very good - atmospheric, well written, etc. But they exist completely outside the story, and at times, harm the story (e.g. you fight and kill Mephisto before seeing him in the cinematic). A lot of this has to do with how the game was developed, and the tensions that existed between Blizz South and North at the time, but considering that the cinematics were developed to be a side-story, it shows. Really shows.
-Warcraft III: Ah, good ol Warcraft III. Pretty much every cinematic is gold. Archimonde destroying Dalaran is probably the weak link, but otherwise, solid.
-World of Warcraft: As far as intro cinematics go, I currently stand at MoP>WotLK>WoD>>Legion>BC>Vanilla>Cataclysm. And to explain, I'll thus say:
-Cataclysm: I really don't care for Deathwing as a villain. It's not to say he lacks depth (e.g. him once being Neltharion), but being corrupted by the Old Gods doesn't make for a compelling villain when corruption is a pet plot point of Blizzard, and they've done it much better (Kerrigan, Arthas, Aidan, etc.). So as Deathwing bursts out of Deepholme, I'm more like...meh.
-Vanilla: Nothing wrong with this - it does its job of giving us flavor for the world, showing the races, locations, etc. Nothing too special.
-Burning Crusade: Similar to Vanilla, but we've got Illidan and Outland in the mix. The former elevates it above Vanilla, if only for "you are not prepared!"
-Legion: This is very close to Warlords of Draenor for me, in that there's a similar 'feel' to both (dealing with the Burning Legion, either directly or indirectly). However, I'm putting it below WoD because it's far more conventional. It's good, don't get me wrong, in that it marries spectacle with showing how far Varian has come as a character, but the following cinematics go above just being "good."
-Warlords of Draenor: This one has grown on me for two reasons. One, it looks fantastic. I mean, not that the other cinematics lacked this, but WoD feels like a step up in terms of the overall quality of presentation. Two, it feels meaningful. This is the point where alternate Draenor's destiny is changed (death of Mannaroth). This is where Garrosh saves Grom from Mannaroth, repeating the WC3 cinematic frame for frame almost as Mannaroth's body explodes. It's little touches like this that elevate this.
-Wrath of the Lich King: Arthas. Ambience. Music. Syndragosa. The Scourge. Northrend. Do I have to explain this>
-Mists of Pandaria: I know, I know, the world collectively decided to shit its pants about panda people after accepting bull people, walrus people, frog people, hyena people, and everything else from the animal kingdom. But this cinematic is incredible, and you know why? Because it's the one cinematic out of all of them that tells a story. Seriously, watch MoP, imagine you know nothing about WoW, and you understand everything. The human and the green thing are fighting. The panda stops them. The mists clear. Its moral/theme is spelled out, true, but it's a moral/theme that is still told entirely through body language and musical/visual cues.
Anyway, moving on:
-StarCraft II: If SC1 was the true birth of Blizzard as a cinematic powerhouse, SC2 is the next logical step. The sequel that improves on practically everything from the original, and that includes cinematics. Not just the pre-rendered cinematics, but the use of the in-game engine for cinematics as well. From the outset it surpasses SC1 in that the cinematics are integrated into the story, focusing on the main characters rather than nobodies. I can't list every single cinematic in the game, but, yeah. I think the Brood War intro cinematic probably stands as the best SC cinematic regardless of game, but SC2 takes the lion's share otherwise. Quality, and quantity. Things seem to have slid down a bit in Nova Covert Ops, but I'm okay, since it's deliberately low key, while SC2 is space opera.
-Diablo III: Ah yes, my favorite Diablo game (ducks flying object). Now, I will say this - if D2 does one thing better than D3 (I'm sure people will argue a lot more, but whatever), it's that its cinematics do establish a darker atmosphere. However, D3 works better in that its cinematics are far more integrated into the plot, as we focus on Tyrael and Leah. They look amazing, function amazingly, and the 2.5D cinematics (fun fact, a new tech was developed just for these) also works much better. It's no secret that I consider D3 to be the best game of the lot, story included, and while D3 doesn't impact me on the same level as SC2 or WC3 in its cinematics/story, it's still damn close.
-Heroes of the Storm: Hah hah...yeah, reused assets anyone?
Seriously, this one is weak. Compare it to more recent League of Legends cinematics, how they tell a story without any dialogue. I know nothing about LoL, but I can still get the gist of what's going on. HotS's intro is incredibly weak compared to them.
-Overwatch: We're at the point where Blizzard might as well be making movies. But I'm not slagging it. There's been a precedent for this ever since The Burdens of Shao-hao shorts - shorts that were eventually mimicked in StarCraft, and ones I think have potential for Diablo as well, using the same 2.5D style. But yes, Overwatch does something else, and you know what that is? Makes its cinematics function entirely without context from the game. And unlike D2, I feel this works. It works because the intro cinematic is self-contained, tells its own story and theme, and does it excellently. Like MoP, it isn't subtle (being honest, subtlety hasn't been Blizzard's strong suit), and the cinematics that have followed have been top notch. Cheesy and cliched at times (see Dragons), but still very good. There's a reason people are clamoring for an Overwatch movie, and it's easy to see why.
And for the record, Intro Cinematic>Alive>Recall>Dragons, so far.
