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Which insects are suitable for children to have as pets?

Ants (Order Hymenoptera)
Ants make great pets
You can buy an ant farm for under $30
Very little maintenance is required
They eat virtually nothing yet are active all the time and perform remarkable feats of tunnelling. They are great to watch and learn from.

Stick insects (Order Phasmidae)
Very interesting when newly hatched, they are active and fun to watch.
As they grow they become much less active and look like, well, sticks. Children?s interest is likely to wane as the insects become more and more static. Require fresh vegetation on a regular basis.

Crickets (Order Orthoptera)
Crickets can make very good pets. The many different species vary considerably in their appearance and show quite a bit of sexual dimorphism (that is, the males and females look different)
They can be quite active, particularly at warmer temperatures and some will sing, given the right encouragement. Require fresh vegetation on a regular basis.

Bees (Order Hymenoptera)
Definitely not for children. Bees are fascinating to keep, and can earn you a little money, but require a good deal of equipment, and care.

Cockroaches (Order Blattodea)
Some parent might blench at the thought of cockroaches in the house but, provided they are properly caged then they are the same as any other insect.
Very active, may show cannibalistic tendencies if food is short, and which some children might find upsetting. Will eat pretty much anything. Hissing cockroaches are very impressive insects.

Millipedes (Order Myriapoda)
Interesting to watch but can spend long periods in an inactive coil, which is pretty boring for children.
Prefer warmer temperatures. Eat detritus. Giant millipedes can be up to 12" long and as thick as your finger so you will need a large tank or terrarium.