Chain Stay Protectors have been around for a long time now and work well on most types of bikes. Some Trail and Jump bikes come with them from new but many don't.
The best known brand for chain stay protectors is probably Lizard Skins but brands like Setlaz have been around for much longer. Both brands use either neoprene or Kevlar as their protection materials. These materials are fantastic at protecting the frame against the chain and the damage it can cause when repeatedly tapping against the paint work as the bike bumps over uneven ground.
Shimano were probably the first brand to come out with a chain stay protector. They used to supply a sticky rubber strip known as the 'Shark Fin' with new bikes back in the 80's. These were a moulded plastic strip with a fin near the front which helped to keep the chain from dropping off the chain rings and getting stuck between the chainset and bottom bracket.
As frames changed shape and more and more had a yoked (squared) chain stay the shark fin protector fitted fewer bikes and something more versatile was needed. This is when chain stay protectors came out. They are available in various colours and widths with Velcro fittings. You then simply wrap it around the frame under your chain. The Velcro works well and keeps them still in all weathers and when filthy you can remove them and wash them.
Now with varying styles of bikes from Road to Downhill along with wheel sizes ranging from 26" to 29" on mountain bikes there are dozens of sizes to ensure you get the best fit.