There are loads of websites like the one posted by chomank. You can find one by simply typing 'Download Youtube vids Online' and most, if not all will use the same system as chomanks, by entering the URL of the video you want to recieve and hitting 'go'.
If you want to put these videos on a device like an iPod or if you do not have a program which is able to play the videos because they have a different extension, you'll need to find a piece of software (downloadable or I'm sure you can find an online service) to convert them to a suitable format.