There's a couple of things to concern about when cleaning the inside of your case.
First, beware of static. An electrostatic shock can fry some delicate components so don't wipe any circuit boards. Canned air or even a leaf blower is safer.
Second, when using pressurized air you should not let the fans spin. There's two reasons: First, the fan may spin overspeed burning the bearings. Second, a fan spinning with external power is a wind turbine pushing electricity backwards into your system. Yes, building your own wind farm is that easy, just some fans in a windy place!
Thus, the safest way to clean your system is to block your fans, use compressed air to remove dust from the circuit boards and vacuum/wipe the dust from plain surfaces. Many modern cases also have a detachable filter both inside the front panel and under the air intake of the PSU in the bottom. Cleaning the filters regularly is a must in a hairy pet household. A wheeled cart to lift the case off the floor is also surprisingly efficent, even better if there's a mesh instead of a solid base under the PSU. Hint: They sell grille carts for flower pots!
