Not Reef Tank Suitable
Not Suitable for Fish-Only Tank
Turf algae is a somewhat broad category consisting of many different forms, i.e., finely branched delicate structures; short and stubby tubular forms; thick grass-like mats; and, both low and/or tall growing forms consisting of leafy lettuce or cabbage-like structures. And depending upon the species, most are not looked upon as desirable, however, some do have useful purposes such as nutrient export and in small "controlled" amounts may look quite pleasant.
Some of the more interesting "green" species have thicker branched growth than what is generally referred to as hair algae, and they include Cladophora, Chlorodesmis, Cladoporopsis, and Valoniopsis. These have tubular filaments and grow similar to clumps of grass. Since the species within these genera are not palatable to most herbivorous fishes, it generally spreads, especially in older nutrient rich aquariums.
There's also Ulva, and species in this genus are usually referred to as "Sea Lettuce." They have soft sheet-like leaves that can grow rapidly in nutrient rich environments, and also just as quickly disintegrate. It's a tasty food for herbivores, but best suited for refugia or slow flowing alga turf filters.
One rarely seen and difficult species to manage for any length of time is Acetabularia crennulata, sometimes called Mermaids Cup. Nice looking yet requires extremely good lighting for this shallow water species. Usually dissipates quite rapidly in most aquaria.
There are also brown and red turf algae, so checkout these groups.