Algae can be an aggravating problem for a saltwater aquarist, but it can easily be controlled with the addition of saltwater algae-eating animals. Reef tanks require the fish keeper to be a bit more selective with these additions, as some avid algae eaters will also graze on corals and be more damaging than helpful to the tank ecosystem. Always check the compatibility of any potential new addition with the fish and invertebrates already residing in your aquarium to avoid any potential negative consequences (fighting, territorial issues, food competition, etc.).
There are several saltwater fish that subsist entirely on plant materials, and for some of these algae is the major component of their diet. Blennies are the best choice, by far, because they are small and spend their entire time scouring corals and glass for algae. Tangs and surgeon fish are also good choices because they are community-friendly (being herbivores), although some tangs do grow to a relatively large size.
If you have a diatom or hair algae problem, the addition of a foxface rabbitfish will clear this up in no time. The foxface will also easily transition to flake-based foods (which some other saltwater fish don't do so readily).
If you are short on tank space or simply don't want too invest in more fish for your tank, another option is to introduce some snails to your saltwater setup. Some of the best are turbo snails, astraea snails, trochus snails, nerite snails and the large abalone. These snails are reef-safe (they won't graze on corals) and will keep the bottom and walls of the tank clean. They eat detritus as well as algae, so they are great for planted tanks as well.
Another great choice for your saltwater tank is a crab. Hermit crabs and emerald mythrax crabs spend their days scavenging for food and are great algae eaters. They aren't always the best companions, though, as hermit crabs will fight for shells and may cause problems for larger snails in the ecosystem. The emerald mythrax crab is very hardy and can survive in almost any tank environment. It is a scavenging omnivore that is especially effective against bubble algae.
The oddballs of the saltwater community, tuxedo urchins and sand dollars, are also effective algae controls. Although they move slowly and won't clear a tank in a short period of time, the addition of a sea urchin or sand dollar can give the tank a new focal point. Sea urchins are interesting creatures with a tendency to devastate an aquarium if left unchecked. They need to be watched carefully because they will feed on many invertebrates and even attack coral if there is no algae on which to graze.