That really depends on the type of filter you have, size of tank, number of fish, among other things.
Cannister filters require very little maintenance. For the first time after 8 months of continuous operation, I gently rinsed out my cannister filter pad and media baskets with dechlorinated water.
power filters have cartridges and biowheels. When I notice water flow bypassing the biowheel, I gently scrub the cartridge in dechlorinated water. I only replace the cartridge when it starts falling apart.
My sponge filters get swished around and squeezed out in dechlorinated water about once a month.
Gravel vacs are essential to prevent uneaten food and fish poop from sprouting fungus. However, people who have heavily planted tanks don't gravel vac much because live plants appreciate the extra fertilizer and because gravel vacs can damage the roots.
I scrub the inside tank walls and gravel vac as best I can (without moving things around) once a week. I'd guess that once a month, I yank out the plastic plants and give them a good scrubbing with hot water. Once in a while, I remove a few big rocks and scrub them under hot water too. I do this to remove algae and brown diatoms that make the tank look unsightly.