The biggest game in terms of filesize on the App Store has to be Riven, the resurrected 1997 sequel to point-and-click adventure game Myst.
It weighs, virtually, a gargantuan 1.01GB.
What's more, you'll need roughly 2GB free to install the game.
"IMPORTANT NOTE," screams the App Store blurb for Riven.
"Riven for iOS is a VERY, VERY large application. We've managed to optimized Riven from its original DVD size to little over a gigabyte. Even at that size it's one of the largest iOS app we know of - so PLEASE BE PATIENT - download times and syncing times can be longer!" (sic)
Pauses of up to 10-15 minutes can happen during this process, you're warned.
Game developer Cyan recommends, in upper case, that you download Riven on your PC/Mac and then sync your iPhone/iPod/iPad to transfer the file. Downloading Riven via the wireless connection is possible "but it can take a while". Cyan clocked up 90 minutes using this method with an iPhone 4 and a "strong" wireless connection.