In general all the game cameras nowadays offer different shooting modes such as burst mode, time delay mode, time lapse mode and video mode.
Burst mode determines how many photos are taken during a single trigger (typically up to 6 pictures). Picture delay defines the length of the interval between triggers, typically ranging from 15 seconds to 30 minutes. Newer camera models feature a time lapse mode that takes defined amount of pictures (or videos) with certain delay and compiles a time lapse presentation on your computer from the taken images.
If you are planning to shoot more videos than still pictures you certainly want to find out the video properties of the camera model you are going to buy. Most trail cameras record the videos in AVI and the typical resolution is VGA (640 x 480). Invest a little bit more and you will get a camera that records HD video (typically 720p) with sound.
What you also want to check is the maximum length of video clips. Some cameras are able to record only short, 10-15 second clips, while more advanced models can shoot longer clips (typically up to 60 seconds).