Is there a minimal tank/cage size requirement for reptile?

When you keep reptile as pets, is there some kind of requirement for the tank or cage size?

If so, what are the rules?

How much room do the reptile pets need in order to be happy and healthy?

I know this is my standard answer, but it depends on the species. Weather it is arboreal or semi arboreal, very active or not, ect... The standard rule with snakes is the cage should be at least 2/3 as long as the snake. I think you want the length x width of the enclosure to equal the length of the snake. But if it is an arboreal species, you have to take height into account to. Most lizards need a bit more space, as they tend to be more active. The larger species of monitors and tegus really need large enclosures. Bearded dragons, blue tongued skinks, uromastyx, frilled dragons, etc... even though smaller, still need moderate sized enclosures so they have space to roam, and so that it is possible to provide appropriate basking temperatures as well as cooler areas so the animals can thermoregulate properly.

I knew there must be some kind of rules for the room and space needed for the pet reptiles from my gut feeling.

Although, 2/3 as long as the snake is quite smaller than I would have expected. Don't they even need to stretch to their full length? :p
How high should the enclosure be for the snakes?

Is it the bigger the better?

Well, I don't use the actual 2/3 rule, because total floor space is what matters, I am not sure if I said it so it made sense, I think the best rule of thumb for minimum cage size is:

length of cage + width of cage = length of snake.

This is a general rule, but, if you have a 6' jungle carpet python, and you put it in a 4' x 2' cage, you have 8 square feet, which is fine. With an adult, to an extent, bigger never hurts. And you also have to take height into account with some species. The above mentioned jungle carpet python, if that cage were 2' or 3' high, would be even better, as they are semi arboreal. It can be different with neonates. To big of an enclosure can actually stress them. You will see almost all snake breeders keep the babies in small enclosures or tubs for at least a few months, so they don't have to worry as much about getting them to start feeding.

So the rule is
length of cage + width of cage = length of snake.

I will remember that.

So the height of the enclosure should be 1/3 to 1/2 of the snake length?

Why would snakes get nervous over big space?

Young snakes can get nervous in very large spaces. I think it is a combination of the fact that humans appear as predators, and the larger space is daunting. All snakes should have hides, and if you do put a neonate in a largish enclosure, they should have multiple hides. It helps them to feel secure. I learned long ago, that in the long run, the more places you have for a snake to hide, the more likely you are to see it out and about. If you have a tame established adult animal, that you have owned for a while, and is used to you, you can really give it as big of a cage as you want. Any time you move a reptile to a new enclosure, it can be a bit stressful. So it will take at least some time to acclimate to the new cage.

That is my general rule for minimum cage size of a sub-adult/adult. Height again depends on the species. A boa constrictor or ball python won't utilize the height as much, so i wouldn't consider it in factoring if the cage is big enough, just L x W. They will use it some, especially if you put ledges or shelving of some type in, but it's not a factor in "necessary space". An arboreal species though, you can consider height as a factor. a 6'-7' emerald tree boa could be happy in a 3'L x 2'W x 3'H cage, as long as you have branches and perches at different levels. They will go up and down as much as they side to side. I would say that same cage would be too small for a 6'-'7 boa constrictor though. As a general rule for height for heavier bodied terrestrial species, 1' is actually fine. I prefer more, I think it is nicer looking if you are going to spend the money on caging to spend the extra $40-$50 and get the extra foot of height, and use some type of platforms or rocks the snakes can utilize.