While not as well-known as the Java and Flame mosses of the world, Taiwan Moss (Taxiphyllum alternans) has been growing in popularity in the aquarium hobby for the last 10 years.
It's smaller and it's leaves are thicker than your other traditional aquatic mosses. It's a slow -grower and it will grow outward horizontally.
Much like other mosses, Taiwan Moss can provide a number of benefits to your aquarium- including oxygenation, a place for smaller fish to hide, and filtration. On top of that, it's a really cool plant that can be used for carpeting or tying down to hardscapes.
It's a great beginner plant as it can thrive in low, medium, and high-lighting, as well as a wide range of tank pH. CO2 is not necessary, but as always it will provide a boost.