Legends of Elite
Rumours have always abounded strange 'Easter eggs' in Elite and its descendants. David Braben did nothing to discourage this, in fact: his innuendo strengthened the credibility of these sightings. The legends of Elite have been one of the great factors that have kept fans loyal, even after twenty years.
The Ninth Galaxy
In Elite Plus (aka the 1991 DOS version) it was possible to reach a ninth galaxy by galaxy jumping from interstellar space.
There is a short story based on Elite Generation ships called Nine.
The Elite manual mentions space dredgers. Immense factoryship agglomerates that scour space for debris, especially at battlesites. Best given a wide berth, they have the reputation of being unscrupulous in what they ingest.
Generation ships are huge colonisation vessels travelling through normal space at near-relativistic speed, many have still to reach their destinations. Of those that have, none have attempted to decelerate and have made no effort to communicate with welcoming parties.
Generation ships were mentioned in the manual of classic elite, and even present in the ArcElite version (unverified, but I have seen pictures).
There are many unreachable planets in Elite. Rumour had it, that on one of these the Elite pilots had their hide-out.
Owning a Thargoid fighter
A definite hoax in Classic Elite and Frontier: Elite II. However, in Frontier: First Encounters, the reward for completing the second part of the Argent's Quest missions was your own Thargoid ship, complete with Thargoid lasers - given by the Thargoids themselves. As for Oolite, there is an OXP that allows the player to buy a Thargoid ship but the penalty is a fugitive legal status that you cannot get rid of!
There were a few stars in FE2/FFE that were un-approachable, and which were rumoured to be black holes.
A star which was unapproachable in FFE due to the game not being able to cope with it being a binary star system.
Supposedly, there is a wormhole at the centre of the galaxy in Frontier.
This rumour has been affirmed by David Braben, but no evidence has been found in the source code.
Rock hermits were mentioned in the Elite classic manual, but not present in all versions of classic Elite. BBC Elite didn't have rock hermits, but ArcElite and Elite on the ZX Spectrum had them. On the Spectrum version, rock hermits could be recognised by noting whether an asteroid was tumbling or not. Asteroids that were not tumbling were rock hermits, and would release a couple of fighters if attacked.
In ArcElite you may collect the normal bounty for destroying an asteroid (2cr) but you will not find any mineral fragments. This also counts on your legal rating; killing rock hermits is considered a no-no by the police.
On Oolite, it is possible to dock with a rock hermit, and the Pirate Coves expansion pack turns some rock hermits into pirate hideouts (which can be fatal to approach in a lightly armed ship).
Commander Jameson, hero of the Thargoid wars.
Your persona in classic, your grand daddy in FE2/FFE.
There are at least 50 warzones in Intergalactic Space.
The planet Raxxla. It is fabled to be a gateway to other universes, or at the very least a portal to somewhere else in the galaxy. Many parties actively search for Raxxla, but no-one has ever found it.
The Dark Wheel
A mysterious organisation with many elite members. They mediate in (or engender) conflicts, expose corruption, search for legends and forbidden technology. In short: they are meddling mystics and treasure hunters.