Moss Balls (Aegagropila linnaei), also called Marimo moss balls, is one of the easiest aquatic "plants" to keep. Moss Balls are a special species of algae that grows in some shallow Japanese lakes. The current of the lakes keeps the algae in a ball shape, and movement is important to keep the ball spherical.
A Moss Ball alone is a great option to keep if you're looking for a pet that can be easily kept by children without any special filtration or light requirements. It will happily survive in a bowl and will live for 100+ years if cared for well.
It can be broken up into multiple smaller balls to propagate or can be laid flat and grown into a mat. Keep in mind that this species grows very slowly (a 2 inch Moss Ball is estimated to be approximately 15 years old).
If keeping in an aquarium, this plant will thrive under low-light conditions. Keep in mind that some herbivorous fish will try to eat it. They do best in cooler water (low-mid 70's).
If keeping it alone as a pet, don't keep it near a windowsill. Direct light can scorch the ball, leaving brown spots. It can be grown under normal house lighting. Replace the water every 2 weeks, and always dechlorinate the water prior. Occasionally agitate the water to move the ball around (this will help it maintain its round shape. No special fertilization is required.
(Photo credit "Northern Gecko")