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We study the spectroscopic properties and environments of red spiral galaxies found by the Galaxy Zoo project. By carefully selecting face-on, disk dominated spirals we construct a sample of truly passive disks (not dust reddened, nor dominated by old stellar populations in a bulge). As such, our red spirals represent an interesting set of possible transition objects between normal blue spirals and red early types. We use SDSS data to investigate the physical processes which could have turned these objects red without disturbing their morphology. Red spirals prefer intermediate density regimes, however there are no obvious correlations between red spiral properties and environment - environment alone is not sufficient to determine if a galaxy will become a red spiral. Red spirals are a small fraction of spirals at low masses, but dominate at large stellar masses - massive galaxies are red independent of morphology. We confirm that red spirals have older stellar populations and less recent star formation than the main spiral population. While the presence of spiral arms suggests that major star formation cannot have ceased long ago, we show that these are not recent post-starbursts, so star formation must have ceased gradually. Intriguingly, red spirals are ~4 times more likely than normal spirals to host optically identified Seyfert/LINER, with most of the difference coming from LINER-like emission. We find a curiously large bar fraction in the red spirals suggesting that the cessation of star formation and bar instabilities are strongly correlated. We conclude by discussing the possible origins. We suggest they may represent the very oldest spiral galaxies which have already used up their reserves of gas - probably aided by strangulation, and perhaps bar instabilities moving material around in the disk.