TS1463: iPod Displays a Red "X" IconLearn about iPod Displays a Red "X" Icon
Usually the red x is a sign of a damaged/dead hard drive. If you send it to Apple they won't actually repair it, but instead will do an out of warranty replacement for a flat fee. See this page for pricing: http://www.apple.com/support/ipod/service/prices/
A third party service may be less expensive and they'll actually just swap out the damaged part (the HD in this case). Google "iPod Classic hard drive repair" and you should get a list of options to work with.
As to whether or not it's worth to have it replaced/repair is up to you, your budget, and preferences.
Thanks so much that is helpful. So would Apple replace it with a new iPod or would it be a used/refurbished iPod? I will look into the third party service as you suggested. I appreciate all the information!