Do Nintendo DS game work on a Nintendo DS Lite

Yes. A DS Lite is the same as the DS, but smaller; A DSi is the same thing as a DS Lite but with a few added features. All DS games are compatible with all the kinds of DS, except ones that need the GBA slot (aka Slot-2):

• Original DS expansion paks work in the DS and DS Lite
  
• DS Lite paks only work in the DS Lite (won't fit in original ds, too short)
• DSi won't support any Slot-2 expansion paks.