Square Enix is showing a brief demo here at E3 of Final Fantasy XIII set in some old ruins near the beginning of the game. Final Fantasy and old ruins go way, way back, so that's not exactly a surprising place for some random encounters and turn-based combat to occur. The PS3 version of the game Square demoed had English voiceovers, though the company said the recording sessions for the English dialogue aren't nearly complete yet and there's still a lot of work to do on the localization front.
Anyway, the combat in FFXIII is similar to what you've seen in past games. The active-time gauge--the per-character bar that fills up over time and lets a character take a turn when it's full--is now divided into quarters. It seems like you can take your turn after the first quarter is full, but every subsequent section that fills up will increase the potency of the action you take. It seems like a good but not-too-complicated way to evolve the old active time battle system everyone's familiar with.
It wouldn't be a Final Fantasy game if you couldn't summon mythical monsters to do the fighting for you, and Square showed off a little of FFXIII's version of summoning. When you bring in a creature, it replaces the party member that summoned it. Summons also have a "gestalt" mode where they change form to gain a different sort of attack. To demonstrate, a Square rep summoned the ice queen Shiva to the battle and then made her transform... into a motorcycle.
Shiva turns into a motorcycle.
After the transformation, another party member hopped onto the bike and started driving into an enemy repeatedly. FFXIII looked pretty good before, but I must say I'm a fair sight more interested in the game after seeing the E3 demo.