I'm another one who loved the opening to FFVII - it really threw me into the thick of the action from the start. I didn't know exactly what was going on yet, but boy, it looked exciting. Especially when combined with that opening Lifestream / Aeris cinematic and Uematsu's amazing soundtrack.
The other... well, series, really, would have to be God of War. I'll use Chains of Olympus on the PSP to illustrate my point here. Not only does it look incredible, but again, you're thrown in right at the deep end when an epicly sized monster storms in to attack you. "Oh crap", says I. Gearing up to fight this big bad, when it gets swallowed up by an even more epicly sized, even bigger bad. What I said at that point remains a matter of conjecture, but it certainly wasn't pretty.