The schools I've gone to have always had a standard system for their belts, and that system is used up until black belt.
As a kid, my school did the tape stripes. So you got your white belt, and it took 4 tests to get your yellow belt, during which you got a yellow stripe around your white belt, then a 2nd, and a 3rd, and finally you got your yellow belt. Then 3 orange stripes before orange, 3 purple stripes before purple, and so through green, blue, red, and brown. Then you got 3 black stripes on your brown belt, and then you test for black belt.
Around the time I quit, they were transitioning to the two-tone belts, i.e. green belt, green belt with white stripe down the middle, green belt with black stripe down the middle, then blue belt. I'm not sure how that affected their testing structure, as this is now one less green belt. I run into one of the instructors from that school every time I go to a tournament, so I may ask her if I remember to.
The school I'm at now, the first few belts are pretty quick: you go straight from white to yellow, straight to purple, straight to orange and green. Then you get a green belt with a long black stripe, then blue. At blue, there's a blue belt with a long black stripe down the middle, then a blue belt with a long black stripe down either side (technically it's a black belt with a long blue stripe, and for the first day after they receive their belt the Master ties their belt on them backwards so it looks like a black belt). Red is the same thing, one stripe, then two stripes. So we say Green, Green I, Blue, Blue I, Blue II, Red, Red I, Red II. We also call Red I "senior red belt" and Red II "Junior Black Belt". Once you're a Junior black belt, you just need time in grade, volunteer hours helping with lower belts, and to meet the testing requirements, and you can test for black belt.
Our colored belts can test every two months, and our black belts can test for intermediary (or "gup" ranks) every two months as well. This is, of course, if they're ready. Most people take 4 months on average, some people take 6-8 months to test. Red belts have a minimum waiting period of 4 months. It stretches out more as the belts get higher, especially at black belt.
For the Dan tests, you must have appropriate time. We also only do Dan tests twice a year, outside of special circumstances (i.e. a private test for someone who is moving and won't be able to take the test with everyone else).