According to
Apple, the iPod can play back the following formats:
H.264 video: up to 768 Kbps, 320 x 240, 30 frames per sec., Baseline Profile up to Level 1.3 with AAC-LC up to 160 Kbps, 48 Khz, stereo audio in .m4v, .mp4 and .mov file formats.
MPEG-4 video: up to 2.5 mbps, 480 x 480, 30 frames per sec., Simple Profile with AAC-LC up to 160 Kbps, 48 Khz, stereo audio in .m4v, .mp4 and .mov file formats.
If the files you're trying to play on your iPod don't meet these specifications (and if iTunes isn't accepting your downloaded videos, I'm guessing they don't), you'll need to convert them using conversion software that has been designed for use with the video iPod. Try
iSquint.