TerrariaThe title screen of Terraria is a scrolling screen that is moving leftward. This moving background is the same that is within the game, but because the background only moves based on the character's actions, I've only been bothered by the title screen. Generally I can navigate the menu quickly enough to avoid much sickness.
Card City NightsIn deck editing screens, deck selection, and victory screens, the background scrolls diagonally. When I originally played this game, I wrote an email to the developer Friday night, and continued playing. The game was interesting enough to grin and bear it thought the sickness. Within a business day of receiving my email, the developer added a setting to their settings file that disables background movement.