And I'm not talking about insects. In what kind of environment could a large number of different species all develop six legs/limbs/appendages the same way most vertebrate species on Earth have four? Could it just be up to chance or is there a reason all animals on Earth have =< 4 limbs?
While not directly related, a couple of the answers here relate to your question.
To paraphrase, I think it has a lot to do with evolution. If you assume it takes hundreds or thousands of generations to evolve a functional limb, its pretty unlikely that it would happen (unless you're selecting for it while breeding). As a result, there's practically no chance for a new limb to be added via evolution.
I have no background in biology or evolution, but given the large # of generations needed to add a limb, vertebrates having 4 limbs +/- a tail is probably related to a common ancestor that crawled out of the sea. (even dinosaurs tended towards this)
Invertebrates appear to have a few more ancestors, but given the general presence of an exoskeleton and weight limitations on land, their overall size was limited and depending on the specific configuration they concentrated on a few body types.
So if you want lots of things with 6 limbs, tie it to a common ancestor. You may also need to show why it was beneficial to keep 6, as humans have less useful feet as compared to a lot of other primates. A couple examples might be -
Terrain - using 4-5 hands to hang onto terrain features and 1 or 2 to harvest resources might be better
Other animals - If most things have 6 limbs and can fight with 4+, you will probably survive better if you can also fight with 4+
Specific resources - you might have 2 legs, 2 large arms to do 1 thing and then 2 small arms for another thing if that series of actions is required to access your food source. This could also be a justification for something like 1 set of human hands, 1 of human feet and 1 of cat/dog paws.
I have vague memories of a biology lecture back when I was a student which said:
- The most efficient way for a fish to generate thrust when swimming is to curve its body into a sine wave. Or some whole number of sine waves. So 2 is fine, but 1.5 or 2.5 is not.
- The most stable arrangement of paired fins on a sine wave curved fish is 2 pairs of 2 (4 fins total) for a single sine wave. By paired fins it means the pectoral and pelvic type which stick out sideways from the body, not the dorsal or anal fin.
- Hence our fishy ancestor had 2 pairs of fins for efficiency reasons... and land vertebrates ended up with 2 pairs of legs. (Presumably by this logic 8, 12 and other multiples of 4 are also stable configurations?)
Apparently Manta rays are the only living species of fish with three pairs of fins: pectoral, pelvic and cephalic. The cephalic ones are the ones which stick out at the front and are used for feeding.
If you can figure out a reason for a manta ray to come out onto land, perhaps its descendants would have 6 legs. But it would have to evolve another way to feed if it stopped using its cephalic fins for that.
Tetrapod lifeforms on planet Earth have four limbs (that's why they're called tetrapods) because they evolved from fish with four fins. See DrBob's answer for more details.
If the lifeforms that colonised the land on planet evolved from benthic or bottom-dwelling ancestors instead of free-swimming fish, then it is probable that instead of adapting four fins of a fish into four limbs of a tetrapod that the six appendages of a bottom dweller developed into the six limbs of a hexapod.
If the planet had a higher gravity than Earth's then the presuption would be that this further weighs the evolutionary dice in favour of six-limbed lifeforms. Since the OP's planet has low gravity, but there's no reason why that benthic creatures might not be able to make the transition to land dwelling lifeforms with lower gravity. Perhaps being able to do so with greater ease than on higher gravity planets.
Interestingly octopuses are known to come out briefly on to land. There are stories of them climbing trees. Octopuses are well known for escaping from their tanks in aquaria and research laboratories and invading nearby tanks full of fish which then become less full of fish. The cunning blighters return to their own tanks and act innocent.
The best explanation is here. Any organism capable of feats like this is a probable ancestor for land-dwelling creatures. While the octopus has eight limbs, it is an easy step to imagine the same thing happening with a six limbed sea creature.