It definitely depends on the type of tank you have, the amount of fish in the tank, the type of fish, amount of live plants, and if you dose ferts or not. I know that if I didn't dose ferts in my heavily planted tanks, I could go longer without water changes. But, since my 29g has a high fish load, I wouldn't go longer than 2 weeks.
My tanks vary a bit.
In my 55g (lightly planted community) I am overstocked, so I change 40-50% weekly. I have plants in there, but not enough fast growing to keep up with the fish load.
40g high tech planted I change 40-50% weekly. I dose ferts, so don't risk nitrates building up. Fish load is low right now, so when I don't dose regularly, I can go about 10 days between changes if needed.
In my 29g (high tech planted community), I change 50% weekly. I dose ferts and to keep things like nitrate from building up, I do a large change weekly. I also have a fairly high fish load in here.
In my 20g (moderately planted Celestial Pearl Danio and Cherry Shrimp tank) I change about 20-30% every other week (sometimes weekly if I have time). Shrimp don't like sudden changes in water parameters, so I do every other week for them. Plus there are tons of stem plants and the shrimp and fish don't make a ton of waste. I don't dose ferts hardly at all, so no risk of building up nitrates.
In my 10g Multi tank, I change about 30-40% every other week. There are only 2 fish in there at the moment (more coming!), so they don't make a ton of waste.
Betta tank is about 20% weekly.
I feed my fish every other day to every 3 days, so in most of my tanks I could go a tad longer than weekly, but I wouldn't go more than 2 weeks in any of them.
As far as gravel vac'ing goes.....most of my tanks are heavily planted, so I just hover in the areas where I can get debri and waste.....otherwise I just change the water. If I had regular gravel, I'd do deep gravel vacs weekly in nonplanted tanks/areas because that stuff is nasty.
With sand, hover over it to get what you can. I do this with the sand in my 55g and 10g. You can see waste and debri alot easier with sand, so you will want to get those out....its motivating.
edit: forgot my babies! In my 5.5g fry tank, I change about 10% of the water every other day to every 3 days. Fry need more frequent water changes to grow well.