Honda's FIT & HR-V models I've tested all allow the front seat to fold flush with the back seat IF you lift the rear seat, match with front seat's back (with headrest removed) and push them down together. Most FITs allow this easily as do some Accords. Toyota doesn't make a solution anymore, but the Prius V and Scion xB both fit the bill. My wife found the rear seat of the xB and the FIT more comfortable than that of the Prius V. Her favorite solution was the Odyssey, but we don't need a minivan anymore.
Nissan Sentra seats also fold flat without a struggle, while the Altima and Rogue come very close to flush with some effort. Mazda 5 is another option, as are Dodge Caliber & Journey allegedly. I'm also told the Lexus IS300 sport cross's front seat folds flat like the Matrix. I haven't found one to test yet!
As a general rule, leather, power passenger seats won't fold all the way down. The only exceptions I've found are Accords. Couldn't find a Hyundai, Subaru, GM or Ford that complied, though I've read of a few trucks & SUVs that will. Didn't find a European car with a front seat that would fold flat; with most you can't even remove the headrest!
Other than the FIT--which advertises a "safely parked" refresh mode including the driver's seat--I only tested passenger seats. Don't know if driver's seats will fold down flush.