I think my biggest installation was probably The Last of Us on PS3, which was about a 26GB download, I'm not sure how big subsequent patches and DLC was, but that was pretty hectic.
The game that has taken up the most space is probably Battlefield 3 once you count all of its patches, texture packs and DLC as well. I've deleted it now to make space for BF4, so I can't check how much space it took up.
I only have a 120GB HDD in my (very old) xbox, and I run out of space often, especially when I'm downloading a new game. It's easy enough to go through the HDD and delete games that you aren't using any more though. It even says there's no more space, and says press a button (Y I think), to make space, then it shows you a list of games and how much space each takes up, and you can go into each and delete install files, patches/DLC, save games, etc.
I was running low on space on my PS3 at one stage, but I replaced the hdd with a 500GB one, and it's fine now.





