John went into the city to deposit his money in the bank
We wouldn't say 'the Bank', as we don't mean one singular bank, rather a specific but unnamed bank.
I'd use 'the cloud' in a similar way — it takes the definite article, as you'll be referring to a particular cloud, but there's an ever growing number of public or private networks available that can all be referred to as 'the cloud'.
If you're looking for a collective noun, I'd stick with cloud computing.
Edit: Just to expand on your original post Steve, I'd definitely go with #2, 'the cloud' in this case; precisely because there isn't 'one & only cloud'. When you're using cloud computing in this context, what you're saying is that you're moving systems away from a physical server room in a particular building.
They won't however be distributed throughout every computer on the internet. Instead they'll be hosted in a shared, distributed networked. This could either be privately held with software like Cloud Foundary, or hosted by a company like Amazon or Rackspace.
These are all distinct options though, each which could be referred to as 'the cloud' individually, but when spoken about together wouldn't become 'the Cloud'.