It really depends on the brand itself.
If it was Coca Cola, i'd go for something "young" and energetic, for example, a "runner" game of a surfer that rides the coca cola logo lines (obviously randomly changing to create a challenge, but where the general aesthetic would remain).
For something like a vodka brand, i'd go for something that blends real life with the game, or in short, a mobile based party drinking game. (I created something like that for a Pub chain which involved "forcing" interaction of the players with the pub clients).
In short, the possibilities are endless and essentially depends on the brand, the target market (Kids, Teenagers, Young adults, etc..) and the desired commercial message.