Cyanobacteria. Cyanobacteria are always mentioned along with algae (they used to be called "blue-green algae") because they are photosynthesizing organisms, as algae are, and they create similar problems for us...
"Later for that!" you cry; "Just tell me how to eliminate the repellant crud!"
But, "Know your enemy" I say. Knowing what kind of creature it is will help you control it.
About cyanobacteria. Cyanobacteria are procaryotes, photosynthesizing bacteria. The gulf that separates the procaryotes from the eucaryotes is the most fundamental division of all living organisms. Cyanobacteria fall into the vast first group: the single-celled organisms that lack a central nucleus enclosed within a membrane, containing chromosomes of DNA. All the genuine algae, even the simplest single-celled ones, have a central nucleus that contains their genes; that feature puts them among the eucaryotes. Their cells incorporate discrete photosynthesizing organelles (the chloroplasts), which appear to have evolved from symbiotic photosynthesizing prokaryotic bacteria that were originally engulfed by a larger bacterium but failed to get digested.
To put it another way and simply, cyanobacteria are not related to algae: they're related to the chloroplasts of algae.
Some cyanobacteria exist as unicellular forms, some of which are free-floating, others as cellular aggregates that form mucilaginous sheets and films, and still others as filaments.
Cyanobacteria preceded the first algal cell by hundreds of millions of years. They weren't the very first inventors of photosynthesis — some anaerobic bacteria beat them to it by many more hundreds of millions of years-- but they were the first organisms to evolve a photosynthetic process — a "metabolic pathway" — that released oxygen as a byproduct. The cyanobacteria were hugely successful on the early earth, pearling away in every still saltwater lagoon, building up in slippery mats and slimy surface films, exhaling oxygen into an atmosphere that still scarcely had any. For many millions of years, the freed oxygen was quickly taken up by the still-unoxidized iron at the land's surfaces and the soluble iron that stained the sea's waters brown. Finally, though, these buffers were exhausted, and free oxygen began to build up in the air. The "oxygen pollution" that resulted caused a catastrophic extinction of the earliest bacterial life, which had originally been entirely anaerobic.
I try to remember this gift of atmospheric oxygen, when I'm siphoning the slimy cyanobacterial sheets off my gravel, and I try to feel grateful. But that was then, and this is now.
Nitrogen fixing. At a certain point, probably before there was any free oxygen in the air, some filamentous cyanobacteria, such as Spirogyra, learned to scavenge nitrogen from the atmospheric inert dinitrogen gas (N2) dissolved in water. This was another important metabolic trick.
Nitrogen is absolutely necessary to living organisms. But, though nitrogen makes up four-fifths of the atmosphere, it is locked away. The molecule of atmospheric dinitrogen consists of two nitrogen atoms bound together so strongly that only a few kinds of bacteria have the ability to capture the stable gas, using enzymes that are collectively called "nitrogenase." Nitrogenase molecules are huge and complex, giants among enzymes, built of two twisted and balled-up proteins, that combine and recombine to convert a molecule of N2 to two molecules of usable ammonia, NH3.
Though nitrogenase enables conversion of atmospheric nitrogen so that it can be employed in life processes, it has a fatal weakness; it fails in the presence of oxygen. To protect the nitrogenase from oxygen, many nitrogen-capturing cyanobacteria have evolved special nitrogen-fixing cells encased in thickened cell walls. Certain filamentous cyanobacteria are able to fix nitrogen gas dissolved in the water within these protective calls, called "heterocysts." Consequently, we might manage to reduce nitrate to unmeasurable levels without daunting cyanobacteria. Recent research suggests that filamentous cyanobacteria don't resort to this energy-expensive metabolic technique as long as there's some free ammonia available. Since ammonia is unlikely ever to entirely run out in your aquarium, chances are that very little nitrogen fixing is going on in there, it now seems. One way or the other, nitrogen isn't a candidate when we search for a limiting factor that will frustrate cyanobacterial growth.
Cyanobacteria are astonishingly resourceful in other ways. After all, they've had 3.5 billion years to develop survival schemes. In response to stress, a cyanobacterial cell can contract into a spore, a dry dormant sphere protected by a tough coat, which will blow into any available water. Or, out of water, cyanobacteria in symbiotic partnership with protective, drought-resistant fungus have formed a whole range of lichens. Cyanobacteria have lodged themselves in some pretty specialized environments: one of the cyanobacteria that can draw nitrogen directly from the atmosphere lives only in the intercellular structure of floating Azolla plants, and nowhere else; the symbiosis of Azolla and its cyanobacteria supplements the plant's nitrogen supplies. Azolla doesn't thrive in aquarium conditions, but I'd hesitate to have it in my garden pond if I were trying to keep water-borne nitrate levels low.
Besides the characteristic bluish ("cyan") photosynthesizing pigment, some cyanobacteria have a range of auxiliary photosynthesizing pigments, which make them very flexible about which wavelengths of light they can use. The auxiliary pigments can color the blue-green cyanobacteria yellowish to dark reddish brown to blackish. Don't let these color disguises fool you when you're identifying that slimy film with the rank stagnant-pond odor.
Links. UCal at Berkeley maintains a good brief introduction to the lifestyles and ecology of cyanobacteria at their Museum of Paleontology website.
Purdue University maintains a whole "Cyanosite" devoted to cyanobacteria. It's got a huge photo gallery of cyanobacterial candids, plus a video of a filamentous cyanobacterium withdrawing within its clear sheath to elude a grazing ciliate! 
The ecology of freshwater cyanobacteria might be interesting to you; it's a concern of the Soil Water Conservation Society of Metro Halifax, N.S., who maintain a homepage.
At the height of the Wall Street "initial-public-offering" market bubble, headlined "Species of blue-green algae announces IPO" as Anabæna went public!
Cyanobacteria at Wikipedia.