What is a good way to concisely explain Bitcoin? Often I'm asked to explain Bitcoin to someone and occasionally I come up with something stellar that really nails it, but most times it's a rambling incoherent mess. 

What I would like to see is a short and simple explanation of what Bitcoin is that is suitable for someone non-technical to understand.
Bitcoin is a new kind of money. It's the first decentralized electronic currency not controlled by a single organization or government. It's an open source project, and it is used by more than 100,000 people. All over the world people are trading hundreds of thousands of dollars worth of bitcoin every day with no middle man and no credit card companies. It's a startup currency which has never happened before.

Bitcoin is the first digital currency that is completely distributed. The network is made up of users like yourself so no bank or payment processor is required between you and whoever you're trading with. This decentralization is the basis for Bitcoin's security and freedom.

Email let us send letters for free, anywhere in the world. Skype lets us make phone and video calls for free, anywhere in the world. Now there's bitcoin. Bitcoin lets you send money to anyone online, anywhere in the world for less than a cent per transaction!
Bitcoin is a community run system not controlled by any bank or government. There's no wallstreet banker getting rich by standing between you and the people you want to send and receive money from.

Bitcoin is more efficient than all competing currencies. This will drive its adoption in the same way computers were adopted, in that computers made people more efficient in competing in the marketplace. A currency has value by it being widely used. Bitcoin is a startup currency with a deflationary bootstrapping economy. Its use spreads by providing the speculator incentive. 

Bitcoin is going to be the biggest opportunity for innovation that the world has seen since the industrial revolution. An idea whose time has come.