There are a few different definitions for the term Gray Jedi that are used in Legends. Sometimes they overlap, sometimes they are contradictory (and this probably says more about the people who are using the term than the people they describe)
##Jedi no longer associated with the Jedi Order
Gray Jedi are those who, though having completed the teachings of the Jedi, operate independently and outside of the Jedi Council. They are typically seen as misguided, though they have not necessarily succumbed to the dark side.
–Gray Jedi Robe item description, Knights of the Old Republic II: The Sith Lords
One self-proclaimed Gray Jedi from the Old Republic era is Jolee Bindo. During the Great Sith War, he sided with Exar Kun and fell to the dark side. When he later regretted his actions, the Jedi Council chose not to punish him and instead wanted to promote him to Jedi Knight. Jolee no longer trusted the Council's wisdom and left them.
Well, I assure you, I see more grey than dark or light. I'm just a stubborn old man, tired of the foolishness of others.
–Jolee Bindo, Knights of the Old Republic
Another example in the post-Clone Wars era would be of the Teepo Paladins who believed that blasters should be used alongside of lightsabers in combat and were censured by the Jedi Council. I suspect that the reason was because this made them seem more militant than the Jedi Order usually wanted to present themselves.
##Jedi who were still part of the Jedi Order, but rarely listened to the Council's gudiance
"The so-called gray Jedi have been with us since the beginning. Although they do not break with the Jedi orthodoxy concerning the dark side, they bristle when asked to take orders from the Council. Gray Jedi make compromises, cut corners, and hide their actions from scrutiny, all under the assumption that their experience makes them authorities on policy. They are mavericks who are difficult to control, but can be valued members of the Order after they have been persuaded to follow the established hierarchy."
–Restelly Quist, The Jedi Path: A Manual for Students of the Force
Some members associated with the Jedi Order were viewed as gray Jedi, due to their headstrong nature and rebelliousness from the orders of the Jedi Council. Some considered Qui-Gon Jinn to be a gray Jedi, despite him being an active part of the Order until his death.
[Qui-Gon] Jinn always does things his own way, always sure he is right, always incredulous if we do not see it his way. Some think he is a gray Jedi.
This rebelliousness also kept him from becoming a member of the Jedi Council.
"If you would just follow the Code, you would be on the Council. They will not go along with you this time."
"You still have much to learn, my young apprentice."
–Obi-Wan Kenobi and Qui-Gon Jinn, Episode I: The Phantom Menace
##Alternative groups from the Jedi, especially those who also studied the dark side of the Force
"We are not evil."
"No, the Jensaarai are not, nor are they wholly good."
–The Saarai-kaar and Luke Skywalker, I, Jedi
There were a number of alternative Force groups that were not part of the Jedi, but weren't part of the Sith either. Several that were referred to as "gray" by the Jedi Order include:
- Voss Mystics: An Old Republic species with their own understanding of the Force, who were neither interested in the Jedi nor Sith but had teachings similar to both.
- Jensaarai: An off-shoot created by a fallen Jedi during the Clone Wars, which taught a blend of Jedi and Sith teachings.
- Imperial Knights: A Legacy-era group who rejected the dark side, but were not fully following the light side either and tended to take a more pragmatic approach to how the Force should be used.
##Those who try to walk a narrow path between the light side and the dark side of the Force
I have never met anyone like you, Cade Skywalker. You walk so close to the dark side and yet... You do not desire, even in some small way, the temptation of the power that the Muur Talisman can give you.
–Celeste Morne, Legacy 31: Vector, Part 12
Some Force users such as Cade Skywalker, tried to dabble in both the light side and the dark side of the Force, without embracing either. This was described in sources such as the Jedi Academy Training Manual.