Both the front and rear facing camera on the Exhibit II 4G can capture video. It records at a maximum resolution of 640x480, and video settings are limited to adjusting the white balance or reducing the resolution.
While the phone is capable of taking videos it's obviously not intended for anything more than playing around with. This is not what you want to record a high school graduation or a baby's first steps with.
Videos are saved in the MP4 format, and can easily be transferred to your computer via USB or the Kies Air app. You can even record directly from the YouTube app, which makes uploading to the web remarkably simple.