ISO 27001 is an ISO standard which specifies security practices for data centers, everything from physical controls on servers to audits and periodic vulnerability checks, among many other things.
Certification for this ISO is important for cloud providers and data centers. Amazon, Rackspace and Azure all maintain pages on their ISO 27001 compliance and audit strategy (likely all the others do too, just sampling some here.
I'd like to write a section on what the standard covers so readers know what they're getting or not getting when a cloud vendor advertises ISO 27001 and what they can expect from those security guarantees.