I don't mean due to inconsistency and prop goofs (like O'Brien's notoriously inconsistent depiction).
But field commissions, flashbacks, alternate timelines, Q-manipulations, etc would be in-bounds. It's about how they were intended to appear on screen.
Rank means Starfleet rank, or possibly rank in another contemporary alien quasi-military force.
According to the Memory Alpha wiki, it would be Geordi LaForge.
Geordi has held more ranks on screen than any other Star Trek character: he was an ensign in a flashback in TNG: "Identity Crisis", he was a lieutenant junior grade in TNG Season 1, a full lieutenant in TNG Season 2, a lieutenant commander in TNG Seasons 3 through 7 and the four Next Generation feature films, a commander in the illusory future of TNG: "Future Imperfect", and a captain in an alternate timeline in VOY: "Timeless".
That would be 6 ranks (Ensign, Lieutenant JG, Lieutenant, Lt. Commander, Commander and Captain), and includes all ranks with the exception of the flag ranks (Admiralty).
I'm going to go with Q.
He appears as a Starfleet Lieutenant, a Starfleet Commander, a Starfleet Captain, a Starfleet Admiral as well as an RN Captain, a US Marine Colonel, a WWIII 'Drug Soldier', A Chakuzon Commander (in Q2) and a Napoleonic-era Marshall.
This makes a total of 9 military ranks held, four Starfleet and five others, albeit all are held illegitimately.
Nog seems to hold an unfeasible number of ranks; On DS9 he holds the ranks of Cadet, Ensign and Lt Jg as well as a temporary promotion to Lt Cmdr on board the Valiant. He also holds the rank of full Commander as well as Captain, as seen in the alternate timeline in DS9: The Visitor.
That makes a combined total of 6 Starfleet ranks. The only main ranks we don't see are Fleet Admiral and Lieutenant
While it is sometimes held that Geordi La Forge has held more ranks on screen than any other Star Trek character, Nog certainly is a competitor. Nog is first seen in his cadet's uniform in "Facets" (albeit before formally entering the Academy) and retains this rank until he is promoted to ensign in "Favor the Bold". In the series' finale, "What You Leave Behind", he is promoted to lieutenant junior grade. However, while serving on the USS Valiant in the episode of the same name, Nog was assigned the duties of chief engineer with the rank of lieutenant commander by acting captain Tim Watters. Furthermore, in the alternate timeline of "The Visitor", Nog was seen first as commander and then later on as captain. In all, there are six ranks: cadet, ensign, lieutenant junior grade, lieutenant commander, commander, and captain, thus equaling La Forge's number. - Memory Alpha: Nog
WORF
11 to 14 ranks
Starfleet:
Ensign (DS9/TOS Crossover: "Trials and Tribulations")
Lieutenant (TNG episode: "Encounter at Farpoint")
Lieutenant Jr Grade (TNG episode: "Evolution")
Lieutenant Commander (TNG movie: Star Trek Generations)
Commander (DS9 episode: "Way of the Warrior")
Starfleet Parallel Universe:
Commander and First officer of the Enterprise-D (TNG: "Parallels")
Mirror Universe:
Regent (DS9: "The Emperor's New Cloak") (both political and military position, commanded flagship of the Alliance) Look under heading Mirror Universe: https://memory-alpha.fandom.com/wiki/Regent
Gowrons Klingon Defence Force:
Weapons Officer (TNG episode: "Redemption")
Captain Worf "...whom attained the rank of Captain (in Worf's case, through the Klingon Defense Force) while under the command of Captain Jean-Luc Picard." See paragraph under heading Captain: https://memory-alpha.fandom.com/wiki/Starfleet_ranks
Klingon:
Commander and First Officer IKS Rotarran (DS9: "Soldiers of the Empire")
Chancellor (DS9 episode: "Soldiers of the Empire") (The chancellor is both politically head of the high council and the military head of the Klingon Defense forces outranking all generals)
Other Possibilities:
If you include Ambassador(s):
Ambassador to Qonos (DS9 episode: "What you leave behind")
Starfleet TOS:
Colonel Worf of the Klingon Imperial Forces (Star Trek VI: The Undiscovered Country) (This is Worf's grandfather who is a different entity, but so is a person in a parallel or mirror universe. He is called Worf and has the same actor playing him)
Q's Universe
Squire (TNG episode: "Qpid") (A squire is a military rank, it is the second lowest rank just below becoming a knight) https://en.wikipedia.org/wiki/Squire
So anywhere from 11 to 14 depending on what you consider a rank. Clearly Starfleet, Parallel, Mirror Universe, Gowron's Defense Force, and Klingon would count. Colonel Worf you have to decide if he's the same character, since it is in name & actor, but not the same entity. Ambassador does have power and was a promotion from commander, but is not necessarily a rank. He was chancellor albeit for a brief moment before he gave the office over to Martok. Chancellor is head of the Klingon Defense Force and highest held military rank. Squire should also be considered. In the Robin hood episode he was Will Scarlet who in many Robin Hood stories is considered a squire.
Why I suggested you might think about including ambassador:
As high-ranking official representatives, Federation ambassadors have powers to issue orders and special instructions to Starfleet starship commanders. (TOS: "A Taste of Armageddon"; TNG: "The Host", "Data's Day"; DS9: "The Adversary") https://memory-alpha.fandom.com/wiki/Ambassador
Klingon Defense Forces Rank Emblems(added since people were questioning Worf holding various ranks in the Klingon Defencse forces):
The rank system of the Klingon Defense Force bears some resemblance to various Earth ranking systems. A ceremonial sash of varying design and material is worn by commanding Klingon warriors to show rank and status in society. The sash can be made of many materials, most commonly of gold thread or silver metal, such as those worn by Worf and Martok. https://memory-alpha.fandom.com/wiki/Klingon_ranks
Klingon Defense Force Hierarchy:
The system of hierarchy aboard ships within the Defense Forces was highly structured. According to one of their systems, one that operated successfully for centuries, the first officer of any Klingon vessel had the duty to assassinate his captain when and if the captain became weak or unable to perform. It was expected that his honorable retirement should be assisted by his "first". The second officer also shared similar duties with his "first". (TNG: "A Matter Of Honor"; DS9: "Soldiers of the Empire") https://memory-alpha.fandom.com/wiki/Klingon_Defense_Force
List of Klingon Defense Force Personnel:
WORF https://memory-alpha.fandom.com/wiki/Klingon_Defense_Force_personnel
(As a side note Worf is working on a project to do a new Star Trek series(God please make it happen) called "Captain Worf." So if that happens then the answer would change to 12-15 ranks adding Starfleet Captain. Here's a link to an article on it from this year http://spinoff.comicbookresources.com/2015/06/11/with-fan-support-michael-dorn-hopes-captain-worf-will-be-star-treks-next-frontier/)
I'm going to post this and maybe someone can fill it out.
It's possible Wesley Crusher appears as six ranks.
It would depend on the following suppositions:
Different levels of cadet count as different ranks. The evidence for this: (1) cadets of different levels appears to be able to give lower-ranking cadets orders (see Red Squadron), and Locarno refers to 'anyone under my commands' and (2) they wear different numbers of little black bars similar to rank pips, which apparently indicate their year in the Academy.
Cdt. Crusher appears with zero or one pip. I'm not certain of this, but I suspect it to be true. It think there is a reveal of him in uniform after he hears he is admitted to the Academy.
Acting Ensign and Ensign are different ranks.
If we accept those premises, then Crusher appears as:
Acting Ensign, Ensign, Cadet grade 0 or 1, Cadet Grade 2, Cadet Grade 4, and Lieutenant.
That is six.
