I know, I know windows media player, win DVD and Power DVD all will play Vob files. The problem I'm having is with files I've ripped to my harddrive. The files play fine, but I can't seem to ...

Audio and video files stored on this old players had different file extensions than your Android files. DAT is a file extension mostly found on video CD whereas, VOB is mostly found on DVD disks.

It will play on your Mac just as if it was the original DVD. With the right tool you can also play the individual VOB files. That tool is the free, open-source VideoLAN Client (VLC).

I have a 1Gb video, in VOB format, on my computer, which I want to play on my iPad1. Can you recommend a free download, which will let me watch the movie on my tablet?

I'm pretty sure it can't play DVD/Blu-Ray structures (all those .IFO files), but it MIGHT be able to play a stand-alone .vob. I'll try to remember to check tonight.