Thanks, never knew it was based on a short story, will look it up. 
What about those “Forget Me” people on ST: Voyager.
Who are they called? I forgot.
Pohl’s Heechee hid themselves “inside” black holes, somehow, to escape drawing the attention of a “bad guy” species they call “The Foe”. Those damn meddling humans forced them to reveal themselves.
The Eternals from Asimov’s “The End of Eternity”.
The Solarians, in Asimov’s “Foundation and Earth.” (Yes, I know they were originally introduced during the Robot series, but there, they’re part of the greater Spacer uber-community, it’s only in the centuries/millennia following the Robot books that they become total hermits.)
I don’t think they really count. First off, they’re not really an alien race, they’re a group of humans. And though they might not want any of the ‘timers’ to know of their existence at all, that would make it hard for them to recruit new Eternals - they even assist the timers in trading valuable goods from one century to another - where it won’t disrupt the flow of time. 
I thought about Niven’s Puppeteers, but they actually aren’t quite paranoid enough to fit the OP. :eek:
The Silence occurred to me, also. Their entire m.o., at least so far as has been revealed, is to manipulate civilizations while remaining completely undetected by that civilization or unremembered by those who do happen to encounter them. They are essentially the “Men in Black” concept taken to it’s most malignant extreme.
Assuming, of course, that any still exist. 
The good super race: the Arisians. The bad super race: the Eddorians.
Also, in the YA novel Enchantress from the Stars, Elana’s (humanoid) race worked to help less advanced peoples (whom they called Younglings) but in secret, so as not to interfere with their development. I don’t believe their race’s name was ever revealed.
Also, in ST: TOS, the alien race who trained Gary Seven in “Assignment: Earth.”
Humans…if they know what’s good for them!
As I say, it’s surprisingly short. It’s online here:
http://www.scribd.com/doc/43784308/8-O-Clock-in-the-Morning-Ray-Nelson
Nelson claims to be the inventor of the Propellor Beanie, and of the character “Beany” used by cartoonist Bob Clampett, who wore one:
Hey thanks, Cal! Now the rest of the day, I am going to worry about phone calls.
heh heh heh
No seriously, that was quite obviously a seminal work. Quite spare and to the point, like the very best pulp SF is.
Also, the Observers, from Fringe. They’ve been hiding for centuries and it’s only been through the advent of photography that anybody ever noticed people in snap-brim hats at the Inquisition.
Somewhat related, and published much later, the Shrouders in Alastair Reynolds’s excellent, Revelation Space, live in folds of space/time known as Shrouds. Why? (Go read it before you open the spoiler; the first book is well worth your time and effort) Turns out they’re a thought-to-be-extinct race hiding from a group of nanotech machines that eradicate all life that gets above a certain level of sophistication. In the RS series, humanity is just about at that level. They manipulate a high-status human to try and attract the attention of the machines, in order to determine if it’s safe to leave the Shrouds. Naturally, they don’t tell him that’s what will happen…
I wouldn’t call it seminal – Eric Frank Russell’s aforementioned Sinister Barrier preceded it by a quarter of a century, being serialized in the first issues of Unknown back in 1939. And it covered the topic at greater and , to me, more satisfying length.
Thanks for the reading suggestion!
Are the rest of his books in that series any good?
The Bill Pronizini short story, “Dry Spell” from 1970. A synopsis is below.
SF writer John Kensington has a terrible writer’s block. Then an idea comes - aliens are building a mind-control machine to conqueror Earth. At its present development it seeks out the minds of those who have stumbled upon their plans and erase all memory of them. He also comes up with a perfect method of defeating the aliens. Seconds later he no longer remembers the idea for his new story.
The second one, Redemption Ark, isn’t bad. The third one, Absolution Gap, is total dreck. He also has a few novels (Chasm City—excellent and film noir-ish; The Prefect—decent) , novellas (Diamond Dogs, Turquoise Days), and short story collections (Galactic North) set in the universe.
RS is really slow to develop, lots of characters and the author’s one of those people who thinks the reader should be able to figure it all out for them self. This can be annoying: "Who is this guy? What’s going on? Why should I care again?
The whole universe has a Gothic, fantasy tone that I found appealing. No FTL, lots of genetic manipulation/body modification, no end of body horror. I’d love to see what a really talented film director and art director could do visually with his setup.
If you wanted a quick intro to the universe, I’d start with Galactic North and then hit Chasm City. Or, you could dive right into Revelation Space, though the plot does take awhile to get rolling.
Yeah, but he eventually stopped bothering to erase everybody’s minds, so now they all remember he’s sentient. They still treat him like a pet because he’s cute. Especially when he wears his little suit.
I thought of the Paxans first, too.
The alien detective and the criminal he’s pursuing in the great 1987 B-movie The Hidden qualify.
The alien hunter in Predator is trying to keep a low profile as he (it?) indulges in his sport.
Joe Haldeman wrote a short story - I can’t remember the title - in which aliens were surreptitiously messing with Earth’s climate to make it more comfortable for them.
The Karrank% from David Brin’s Startide Rising could fit the bill.
What about the Dowd from that TNG episode? The one that killed all Husnock with a single thought?