How to identify if a video is 720p or 1080p?

In VLC you can read this from the "codec information" dialogue, access via the tools menu, which lists among the information presented the video resolution.

Be aware that the 720p/1080p only refers to the height though, and many wide-screen videos will seem smaller by this measure as the bars you see at the top/bottom are not encoded in the video stream, so you may need to look at the width instead. For instance a video intended to be full-screen at 16:9 (~1.78:1 - the most common aspect radio for a wide-screen TV) will be 1280x*720 but a wider wide screen video (films often use ratios like 1.85:1 and 2.35:1) might be 1280*545 (for 2.35:1 - it would be 1280*720 if the black bars to make the picture match the 16:9 ratio were encoded into the video stream but they are usually not unless you got a cap from an encoder who doesn't know what he is doing).

For most video formats you can gain similar information directly from Windows Explorer too: right-click the file in question, pick properties, in the properties box that comes up select the details tab, and you'll find a section headed "video" which lists the frame dimensions, clip length, and other similar properties. If you select multiple files and they have the same value for a property (i.e. Frame Height) you will see the value otherwise it'll display the text "multiple values" instead. For multiple files the length property shows the total length of all the selected videos.

You can use the good old GSpot to see the full specs of your videos.

If you are very much interested in the multimedia information behind any audio or video file, I might recommend you to start using MediaInfo a free software.