I have Marimo moss balls in my tank... they are like furry green golf-balls, solid, not the floaty sort that fry hide in -- sounds like what you're talking about? They are in fact algae rather than moss. But very non-invasive so won't spread.
I bought them for two reasons -- to out-compete the algae & also because in japan they are thought to be very lucky! You are meant to tell the moss ball your wishes and they make them come true. I wished for less algae
One on their own might look a bit weird but I have a circle of them in different sizes round an airstone and they look very pretty.
If you don't wedge them down a bit & they get enough light they can float up and down in your tank as they photosynthesize, as the air bubbles kind of 'stick' in their fur... some people might quite like that though. You can also tie them together or to rocks etc as anchors.
Debris and bits have a tendency to stick to them -- my guppies like nibbling up the leftovers from them but don't seem to eat the moss itself.
I ordered mine off ebay and they were bigger than I expected so broke a few into pieces to see what would happen -- they seem to rejuvenate well into lots of little baby moss balls! Yay!
This site might help convince you of their cuteness.
