When many games are delisted they’re simply removed from the public facing marketplaces where you would have be able to purchase them. In most cases Xbox.com even retains the product page with screenshots and release information while removing all links to buy the game.
Fortunately, previous purchases including demos are maintained in your download/purchase history. You can dig them back up and download them to your Xbox 360 or PlayStation 3. In some cases, especially with promotional apps, the items are completely gone but thankfully those are few and far between. Below are two videos I recorded walking through the process to find and queue up items from your download history for both Xbox 360 and PlayStation 3.
I hope these videos help you get some of your delisted games back!