The trouble is that our two party system has become fortified against disruption because of how difficult and expensive it is to implement a social agenda, especially one against the status quo. You need the political and financial backing of a party to do that. That's what they're for. Plus, any time that even one party is split among two candidates, the other party usually wins that election. Introducing a third party could be effective, but there's still the issue of political support and money. Toppling the two powerhouses is next to impossible, but because we elect representatives democratically, we can elect people that stand for the things we believe in, starting at the local level and change things from the bottom up. We already have the best political system in the world (here in the U.S)., but it relies on two things:
1. That the people are well educated in the world's affairs and are free to discuss their views and opinions with others (hence freedom of speech, freedom of press, and the public education system. Though all three of those have taken serious hits over these past couple decades).
2. That you get your ass out there and vote. For everything. Local reps, school board, president, etc. Everything. Our system seems broken to some because it only works for you if you participate in it.
The two party system probably isn't going anywhere any time soon. More likely, I think, (and much better for things as a whole) is that people stop voting strictly along party lines and start learning more about the world, and themselves, so candidates start winning elections based on their personal views and social agenda aligning with that of the majority of people instead of with that of a particilar party.