Super Smash Bros Brawl. It was already a doublesided game with a large file size to begin with, and then they added multiplayer online. The result was that it was very laggy online and nobody ended up playing the multiplayer.
You've really got no idea how computers work, do you? A game being large in storage size has literally no effect on its playability online. Ideally, only a tiny bit of data, such as for instance the opponent's controller inputs and position, is sent over the network, and the console uses the resources that are already on the disk to display that character on the screen. A game could be a single megabyte, or a dual-layer 8GB DVD, and still send the same exact amount of data over the network in multiplayer.
The problem with Brawl's online mode is that either the programmers didn't optimize the network code well enough, resulting in too much data being required, or that Nintendo's network wasn't set up well enough to handle the traffic from online play. In all likelihood it's a combination of both.
From what I've heard about the Wii U's online service, it seems that those problems should be gone. I don't own one, so I haven't really been able to see it for myself, but if that is indeed the case, then I'm with Trainman. But, of course, if Nintendo deems that spending the extra time to develop online multiplayer for its games won't help them sell, then I guess there's not much that can really be done about it. Kind of a shame.