Damselfish are some of the mainstays in the saltwater aquarium hobby. They are often quite hardy, many stay on the small side as adults and the various species are quite colorful. The Damselfishes all have very different personalities and temperaments so make sure to research the species you are interested in keeping.
Also, it needs to be said that even though many of these damsels are very hardy it's not advisable to use them to cycle a new tank. Let the live rock cycle the tank. There is no good reason to use fish to cycle a tank these days.
One of the best to keep in a saltwater tank is the Green Chromis (chromis viridis). When kept in appropriate numbers and fed frequently these little chromis make an awesome addition to a reef tank. They stay on the small side, look great in groups and won't fight with tank mates. A completely under rated fish in my opinion.
Chrysiptera hemicyanea Azure Damselfish Like most damselfish species, the Azure Damselfish is considered very hardy and often recommended to new hobbyists as a good first fish in new tanks.
Chrysiptera cyanea Blue Damselfish This fish is also known as the "Blue Devil Damsel" due to it's temperament. It's a good thing these fish stay on the small side at around 3 inches (6 cm). Use caution when stocking a tank with these little devils.
Chromis viridis Green Chromis One of my personal favorite saltwater fish species of all time. Photos hardly ever do our Green Chromis friends justice. You just have to see a school of them in person to appreciate their beauty and personality. They are quite peaceful except amongst themselves where you may see tests of dominance within the group.
Chromis cyaneus Blue Reef Chromis Similar in temperament to the Green Chromis, these Blue Chromis do well in schools too and look simply fantastic.
Chrysiptera parasema Yellowtail Blue Damselfish This is a very hardy damselfish and they can be very territorial, even with species much larger than them.
Dascyllus aruanus Three Stripe Damselfish Very hardy and similar to many other damselfish species, the Three Stripe Damselfish too have been used to cycle an aquarium or two. Use live rock instead of live fish to cycle your tank.