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IBM lets you poke around one of their quantum machines here for free:

https://quantumexperience.ng.bluemix.net/qx/experience

They also include a brief tutorial on how to program for it too.

yes! I've been playing around with this while writing this guidebook, and I highly recommend all readers to try it out too, once you've gotten familiar with quantum gates. I'll very likely be adding quantum circuits and their results (from IBM), in an upcoming guidebook discussing some really cool quantum algorithms.

AFAIK this is a simulation, not real quantum machines.

They have both a simulator and real machines you can use. The "ibmqx5" is a 16-qubit device. The problem is that noise rates are very high. For example, just to swap two adjacent qubits (using three CNOT gates), it looks like you will incur at least 10% error. It is hard (though not impossible) to run meaningful experiments on such a noisy system.

https://quantumexperience.ng.bluemix.net/qx/editor

Oh, thanks. You are correct that it is very noisy. Just a single CNOT is giving me 15% error.

Here are the numbers for their latest 20-qubit device. CNOT error rates are a bit lower. I don't know if they plan on making this publicly accessible.

https://youtu.be/T-8uuq7Izl8?t=26m36s

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