Terminator 2: Judgment Day:

Sarah Connor herself decides to explain the first movie, and the background of the second movie to us, while robots slaughter people and her scarred son scowls at us. (That glimpse of Future John packs more punch than five hours of Bale, incidentally.)

Robot Jox:

An all-time classic movie, this Joe Haldeman/Stuart Gordon joint starts out with a gruff voiceover packing everything we need to know about robotic single combat into one speech. With rubble.

Slipstream:

This opening monologue from Steve Lisberger's followup to Tron almost belongs in the "what the hell are you talking about" category. What the Hell? Earthquakes, okay. And then they "merged civilizations together?" But then there's a wind that ate everything. And someone is traveling it. Wha?

2019: After The Fall Of New York:

This one wins extra points for having the synthesizery blues score, and the guy in the trenchcoat pretending that the synthesizer is actually his trumpet. Twenty years after the bombs fell, New York is still a shithole. Sorry.

Doomsday:

This actually isn't the entire opening voiceover of this film, because it continues after about five minutes of people being shot by riot cops. Scotland gets turned into a scabby plague sore, and those sensible Brits wall it off. Which works out perfectly, of course.

Judge Dredd:

Can I just say, I love it when a voiceover comes with a text crawl, in case you need to follow along at home? Most movies do one or the other, but only a truly great movie has a text crawl and a voiceover. The U.S. has gone to mega-shit with Megacities, and a new breed of law enforcer rises up.

City Of Ember:

The movie's entire backstory is compressed into a couple of minutes. Global disaster, underground city, box of instructions... box gets lost. Oh noes.

The Road Warrior:

Thanks to John Hazard for finding this online. Still the greatest post-apocalyptic movie opening of all time.

Directed by Stuart Gordon (Reanimator) and written by Gordon and Joe Haldeman, Jox takes place in a future postapocalyptic world, after some kind of nuclear cataclysm. The U.S. and Soviet Union, now called the Western Market and the Russian Confederation, no longer fight wars to settle their disputes. Instead, they send huge freaking robots into battle, to smack each other down until a victor is declared.

I love the way the battlesuits are depicted, with Alexander moving his actual hand to make the robot's hand reach down and overturn Achilles' tank. The giant robot effects are entirely done using models and stop-motion animation, but they look way better than a lot of CGI I've seen. In particular, you can actually see the fighting robot transforming into a tank — unlike in Michael Bay's Transformers, where the transformations were always so blurry and disjointed that you couldn't make out what was happening. Thanks to everyone who recommended Robot Jox to me — it really is an instant classic.