We collect things and, as long as we attribute value to these things, we want to preserve them. The digital age has changed the way we keep things. To be completely exact, these are not 'things' anymore. We name them data.
Think of photos. I'm 25 and I have printed-format photos of my childhood travels only. I usually don't print photos, my parents do it. My parents used to buy photobooks, I don't - I have a cloud space.
The new generations are completely accustomed with keeping digital the things they are affectioned to. From an environmental standpoint, one may think that we're no more creating dumps of old photobooks and so we are contributing to make the world greener. This is actually true, but how much greener? Probably less than what you thought.
The current ways of storing data have an impact on the environment - Greenpeace has determined that the Information Communication Technologies are responsible for 10% of the world's energy demand (Mark P. Mills, The Cloud Begins With Coal, Aug’13; Greenpeace International, How Clean Is Your Cloud?, Apr’ 12).
The why is simple: what you think is on your cloud is actually in someone else's hard drive and this hard drive needs maintenance energy, especially for cooling. As all the big trends in changes, they're made of frequent methodical actions, not of big rare events. This is the case of the portion of climate change due to cloud computing - it is our actions that fuel it.
Final Thoughts
To conclude, our behaviour with cloud storages should not be much different from what we would do without it.
If you have five identical photos, you print one of them. Similarly, we should keep on our cloud only one of them.
Because having photos on a cloud is not free - at least, it is not free for the environment.