Often confused with the similar Trillium flexipes, the first two photos below are Trillium cernuum. Look closely at the stamens... the anthers and filaments are approximately the same length. In Trillium flexipes, the anthers are much longer than the filaments. The ranges of the two species sometimes overlap, but Trillium cernuum is generally a more northern species, whereas Trillium flexipes is generally more southern.
The photos above are from Bog Meadow Nature Trail in Saratoga County, New York, May 21, 2014.
For comparison, here are four photos of Trillium flexipes. The first was taken at Turkey Run State Park, Parke County, Indiana, May 3, 2008. The next three were taken at Bendix Woods Nature Preserve, St. Joseph County, Indiana - the first two on May 5, 2013 and the last on April 25, 2009. Again, take a close look at the anther to filament ratio. The anthers are much longer than the filaments in Trillium flexipes.
I tend to think that the anther to filament ratio is a better way to distinguish these two similar species than the actual length of the filaments. Many references use a filament length of up to 2 or 2.5 mm for Trillium flexipes in their keys, but if you dissect the flower you often can find filaments that are longer than 2.5 mm. In fact, I would be willing to bet that the filaments in the first through third photos of Trillium flexipes above have filaments longer than 2.5 mm (I can see them pretty easily without even dissecting the flowers).
All of this said, I have seen specimens in northern Indiana that are somewhat intermediate between the two species, so the distinctions are not always as black-and-white as they are in these photos.