From Wikipedia (source is Paramount pictures themselves):
The DVD includes two alternative endings, which vary only slightly. The first alternative ending shows Rob and Beth exiting the Coney Island–Stillwell Avenue station instead of on the Ferris wheel and features different sirens in the background as Rob talks to the camera.
And the Second:
In the second alternative ending, just after the final explosion, Beth can be heard screaming "Rob!", followed by a very brief clip of an unknown person looking at the camera (in the commentary, Matt Reeves said that it was one of the crew members) and brushing rubble off the lens. The film then ends with the original final clip of Rob and Beth on their Coney Island date recording themselves on the ferris wheel as the camera tape runs out, with two differences: there is no timestamp in the lower left-hand corner of the screen, and there is an additional beeping tone indicating the end of the tape.
Essentially, yes, 2 alternate endings exist, but they do not make many changes to the overall plot, just to the perception of this supposed sequel they're making.