The Ethereum project has some ideas for making it so each node only has to see a subset of transactions, instead of all of them. It's not an easy problem.

They and a few other projects also hope to pull off a "proof-of-stake" system that mostly does away with mining. Done naively that can be attacked, but there appear to be ways to mitigate the problem. Initially, Ethereum is settling for a proof-of-work algorithm that's more resistant to specialized hardware, so big central miners can't get such an advantage.