First off, physical access is golden, with physical access to a system and enough time and effort, system administrators can gain access if they don't already have access. This affects situations like co-location (colo) services where a company rents space from the provider in a well-connected data-centre but provides and administers their own system. If malicious the only noticeable activity may be unexpected reboots, while the admin gains root/administrator access.
System administrators of virtual private servers, and shared web hosting have root of administrator access to the entire system. They need it to do their jobs. Now front-line call centre workers may not have administrator access, but a limited help desk type access for common tasks like password resets, etc.
Professional system administrators will not access other companies' web sites and data without purpose. Valid reasons include legal (i.e. law enforcement warrants, subpoena, writ) which may or may not include a secrecy order, technical including server configuration, upgrading, administration, log reviews, and computer / network security - looking for evidence of potential malicious users / attackers trying to gain unauthorized access.
That said, I've only seen co-workers abuse their access for premium content, primarily adult material. And there have been numerous cases of "revenge" unauthorized access of estranged spouses, partners, bf/gf that have made the press.
For the most part, it tends not to be a serious problem, but it does happen.