It probably sounds specious, but I have found having a dog around has made me both more productive and more creative. The evidence for this claim is the number of daily messages I post to our team message board that start with the phrase "While I was out walking the dog I had this idea...."
This is my muse, Archer, the retired racing greyhound.
Before getting a dog I would get sucked into a problem and become obsessed with solving it, the kind of linear obsession that leaves no room for creative leaps. What is needed is to allow the problem to marinate in my subconscious, to facilitate the unexpected synaptic connections that occur when you finally let your mind relax. The problem is, obsession with solving the problem makes this type of relaxed mind difficult and leaps of creativity less frequent. I am sure with practice one could recognize the symptoms and use some type of mediation exercise, but for me the answer is walking the dog. The pattern repeats regularly ... I hit a nasty bug or design conundrum, get stuck, and then take the dog out for 15-20 minutes, and the answer suddenly presents itself.
For me, dog walking seems to engage the kind of subconscious pattern matching that provides the keys to unlock many problems. Wallas would have called this the incubation phase of creativity. I think of it as a cousin to Mihály Csíkszentmihályi's concept of the flow mental state. This seems to be validated by Nardi's work on the neuroscience of personality. Specifically, the brain imaging results where he describes the delta state in terms of Csíkszentmihályi's flow, but adds that "also on occasion when we are copacetic, open to whatever comes next." This is a perfect description of my mental state on a walk with the dog. I feel close to that feeling of flow, but not quite the same -- an approximation. But it seems to do the trick. As a side note, Nardi's brain imaging results of people watching TV shows up as black; similar to a deep non-dreaming sleep. So TV is not so good for creativity ... just saying.
I don't find that walking alone or with another person works as well. I wonder if it is the non-conversational interactions with the dog, just enough interaction to get me to stop focussing on the issue, but not so much that my mind is focussed on keeping up a conversation with someone else. Whatever the reason, it works; almost always presenting a promising new direction, if not an outright answer.