The ideal global warming game, it seems to me, would be a detailed simulation of the global climate as well as the global economy -- and preferably one that would allow you to tinker with the assumptions, both at the macro and micro level. At the macro level, I'm imagining scenarios ranging from "We're all doomed!" to "Bah, the Copenhagen Consensus has it right," and at the micro allowing you to twiddle individual knobs (e.g., "nuclear power plants are safe as houses" to "they go blooey with alarming frequency").
Climate Challenge is not the ideal global warming game -- but it's surprisingly engaging.
It's played over ten turns, each representing a decade. Each turn, you can choose up to six policies, represented by cards, in five categories (National, Trade, Industry, Local, and Household). It's fundamentally a resource management game; your resources are global warming gas emissions, tax revenue, food, water, power -- and public approval. Any policy you choose has impacts on some of these resources, and the goal is to reduce emissions continually without pissing off the voters to the point that they dump you, and without running out of the other resources entirely.
The "policies" on offer are manifold, and some even amusing (e.g., holding the Olympics will make your voters very happy, but has rather disastrous impacts on everything else). Some have light-bulbs printed on their cards, meaning that selecting this policy opens up additional policies on subsequent terms. And some are hard to argue with, having positive impacts for minor costs, and are even popular with the voters (who seem fairly green, all things considered). Of course, there's another resource to consider: You only get to choose six policies each turn, and it's tempting to select minor but positive ones, thereby avoiding harder decisions that will have more powerful outcomes.
Ostensibly, you are "the president of the European Nation," despite the fact that there's no such person and no such nation. Every three years, there's a global summit in which you try to get the leaders of other regions to agree to binding emissions targets; you can bribe them with subsidies to make them more likely to agree. In the game, this is a minor fillip, although in reality, the global trumps the local -- we're all likely to cook in China's industrial waste, after all.
As a simulation, it's not exactly deep, but it does get across the notion that tradeoffs need to be made to reach your goals; and you can certainly quibble about whether the policies presented do in fact have the outcomes they claim. But if a good game, as has been claimed, is something that requires you to make interesting decisions, then Climate Challenge certainly qualifies.