It depends on the type of case and where the computer is located.
I keep my computer
on my desk, in a large room which only I use.
The case is a Switch 810.
The components inside get only very fine dust on them because the rest is caught by the filters.
I clean the filters every 2 or 3 months, and the inside every 6 months.
I can clean inside the case using only a can of airspray, and this is how the main front intake filter looks after a month of use while everything inside is still dust-free:
On the other hand my teen keeps her tower on the
floor and in her
bedroom (imagine a teen's bedroom...)
The case is a pretty but cheap old Aerocool with no filters.
When we clean it we have to use an air compressor and a small paint brush because the layers of dust get caked on the components and there'd be tight balls of fluff hiding in every corner.
It's a PITA to clean, we have to dismantle the front piece which is held only by (now very worn out) plastic clips.
We have to clean it every 3 weeks minimum, because after 4 weeks check photo below!
The case has no filters, and here is how the front intake fan looks after a month of use. You're supposed to see a turbine-like fan there but it's invisible for all the fluff!