You can, but it's generally not worth the effort. They have to be encoded into a special format that really only the DS uses. You can't have the resolution very high, the audio will sound tinny, and you typically have to buy a special media player cartridge that has a MicroSD slot on it that you can load the video on.
You'd be better off getting a PSP if you want a portable game system that can play videos.
Please tell me if i can watch videos on my DSi. If yes, Then please tell me the procedure.