I've encountered this before. It's usually a faulty fan. You have to isolate which fan is the issue. Try unplugging one fan at a time and see if the noise stops, then you'll know which fan is the issue.
Don't unplug the CPU fan though, modern CPU's need their cooling.
Another common noise from crowed cases are when unused molex plugs are up against a fan (especially a CPU fan) and make a louder more abrasive noise. That's why tying them out of the way are the next best thing to a modular PSU, where you only use connectors you need.
Cheap aluminum cases that are too thin can vibrate too, but that's usually noticable only if you have it on your desktop.