In Addition to Mooz's answer which features the now-extinct houses, There are plenty of minor Houses who used to be great once, even royals and still alive.
To clarify, to limit the scope, I will just stick to Houses who used to be Kings once and aren't extinct. If we start discussing houses which fell from Major to minor like House Peake etc, it will be too broad.
Crownlander Houses
They ruled as Kings and fought many wars with rivals in shape of Storm Kings, Massey Kings and Darklyn Kings. It is unclear how they were subdued by Storm Kings. In Aegon's conquest, they sided with Targaryens from the onset and at the war's conclusion, they became vassals of Dragonstone instead of Storm's End. They are a major vassal to Lord of Dragonstone today.
Starting off as vassals of Storm Kings, Masseys eventually broke away and forged their own Kingdom. They were subdued once again by Qarlton II Durrandon who slew King Josua Massey. Josua's daughter however married founder of House Bar Emmon and together they ousted the Stormlanders and restored Josua's son to the throne. They were brought back to Stormlander realm with marriages. After Aegon's conquest, they became direct vassals of the King as part of Crownlands.
Northern Houses
They were Kings once (Called themselves Red Kings) and rivals of Starks for dominance over the North. Numerous wars were fought between the two Kings. Kings Royce II and Royce IV even burnt Winterfell. King Rogar Bolton was last of their royals and submitted to Starks of the Winterfell. From that point, Boltons were reduced to vassals to a Great House. They are still a Major House (Below Royal House/Great House but greater than Minor House). And since ADWD, they're a Great House in their own right.
The ancestors of House Dustin reigned as Barrow Kings. There were numerous conflicts with the Winter Kings of Winterfell which eventually resulted in submission of the Barrow Kings. House Dustin still commemorates that heritage with a Crown in their sigil.
House Umber used to be Kings once. It is unclear how did the Starks subdue them. They are today major vassals to Lord of Winterfell.
House Glover used to be Kings after the Long Night. It is unclear how did the Starks subdue them but it is mentioned that they were subdued by Starks of Winterfell, not some other house. They are today major vassals to Lord of Winterfell.
Valeman Houses
House Royce ruled regions of Vale as Bronze Kings once. Last of their royal line, Robar II, was defeated by Andals under Artys Arryn and bent the Knee. They have since been a vassal of House Arryn.
House Shett ruled as "Kings of the True men" in regions of Vale and fought many battles against the Bronze Kings. Last of their Royal line, Osgood III Shett died in battle against Royces. His Crown was then claimed by his Son in Law, Ser Gerold Grafton and the Kingdom was inherited by House Grafton as well. There are now two branches of the house, both minor and vassals to Arryns.
They inherited crown of the Shetts and continued to reign. It is unclear when were they subdued by Arryns. They are now reduced to landed Knights and vassals to Arryns.
They were Andals who conquered the Fingers from First men and began their domain as mere Lords. At a later point they started calling themselves Kings of the Fingers. They eventually bent the knee to Arryns presumably before the Arryn-Royce showdown at Seven Stars. They are now a major House. They are one of the few houses of Westeros who own a Valyrian steel sword.
House Sunderland briefly reigned as Kings of Sisters when they rebelled against Arryns but the conquest of Aegon soon came their way and they submitted to Targaryens. They are now a minor House.
House Borrel were pirate Kings once until Starks ended their dominion. Borrels are now minor vassals to Arryns.
Riverlander Houses
House Blackwood used to rule Wolfswood in the North but they were eventually forced into exile by expanding Stark realm. They carved themselves a new Kingdom in Riverlands which fell when the Andals came. They are now a major vassal of Lord of Riverlands.
House Bracken also ruled their parts of the Riverlands as Kings and fought many wars against their rivals the Blackwoods. They allied with Blackwoods when Andals came but lost the war. They are now a major vassal of Lord of Riverlands.
House Vance is descended from Armistead Vance, an Andal conqueror who ended the reign of House Mudd on Riverlands. It is unclear how they lost their independence and crown. They are today major vassals of Lord of Riverlands. The House is divided into two branches which are House Vance of Wayfarer Rest and House Vance of Atranta.
House Mallister conquered their domains from the Ironborn and reigned as Kings. They were subdued by House Teague which is now extinct. They are today major vassals of Lord of Riverlands.
Mootons once reigned as Kings of their lands until they were presumably subdued by now-extinct House Justman. They are today major vassals of Lord of Riverlands.
House Charlton reigned as Kings once. It is unclear how they lost their independence and crown. They are today major vassals of House Frey.
Ironborn Houses
Ironborn generally choose their Kings unlike other Westerosi so there have been plenty of Kings from numerous Houses, some of whom are still alive.
Their ancestor Joron I ruled as High King of Iron Islands. The House is still alive and a major vassal to House Greyjoy.
Their ancestor Ragnar Drumm ruled as High King of Iron Islands. The House is still alive and a major vassal to House Greyjoy. They are one of the few houses of Westeros who own a Valyrian steel sword.
House Harlaw gave two Kings of Iron Islands, Erich V and Harron I. The senior branch of the House is now a major vassal of House Greyjoy and has four cadet Branches who are minor vassals.
Their ancestor Urrathon IV reigned as King of the Iron Islands. The House now has five cadet branches in addition to the senior branch located in Hammerhorn. All are vassals to Greyjoys. All are minor except the senior branch.
Westerlander Houses
House Crakehall used to be Kings of their domains before the Lannisters subdued them. After that, Aubrey Crakehall reigned briefly as King of the Iron Islands. The House is now a major vassal to Lannisters.
They used to be Kings of their domains. Last of their Royal line, Morgon Banefort was subdued into vassal by King Loreon I Lannister after a bloody twenty years war. They have since been a major vassal to House Lannister.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings as well until the ever-expanding Lannisters knocked on their doors. King Tommen I Lannister forced them into submission when he raised a great fleet to take their Island Kingdom. He married daughter of King Farman and the Farmans became vassals from Kings. They are a major House in service of Lannisters since then.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a minor vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a major vassal to Lannisters.
They used to be Kings of their domains. It is unclear how were they subdued by Lannisters. They are a minor vassal to Lannisters.
Not technically Kings, but when King Gerold III Lannister died without a male heir, his only daughter's husband, Ser Joffrey Lydden was elected to the throne and crowned as Joffrey Lannister. All current Lannisters are descended from Joffrey Lydden AKA Joffrey Lannister.
Reachman Houses
House Hightower reigned as independent Kings for much of the early days. They fought many wars with the Gardener Kings of Highgarden, the Dornish and Ironborn raiders. Last of their royal line was King Lymond Hightower who put down his crown and accepted suzerainty of High Garden with marital alliance with King Garland II of High Garden. They are today one of the most richest families in the realm and a major vassal to House Tyrell. They are also among the few families who possess Valyrian steel swords.
House Redwyne ruled as Kings of Arbor until their last unnamed King was lost at sea and the throne passed to his cousin, King Meryn III Gardener of Highgarden. They're today one of the greatest naval powers of Westeros and major vassals to House Tyrell.
Stormlander Houses
House Tarth used to rule their Island as Kings once. They accepted suzreinity of now extinct House Durrandon when King Durran the Fair of Storm's End married daughter of the last unnamed Tarth King. They are today a major vassal of Storm's End.
Dornish Houses
House Blackmont ruled as Kings in the early days. They were subdued by House Martell (Officially Nymeros-Martell) after Princess Nymeria of Rhoynar landed in Dorne and forged a marital alliance with House Martell. Last of their Kings was Benedict Blackmont who was sent to the wall by Nymeria. They are major vassals to House Martell today.
House Dayne ruled as Kings of the Torrentine.They were subdued by House Martell (Officially Nymeros-Martell) after Princess Nymeria of Rhoynar landed in Dorne and forged a marital alliance with House Martell. Last of their Kings was Vorian Dayne who was sent to the wall by Nymeria. They are major vassals to House Martell today. Their ancestral sword Dawn is just as famous, if not more, as Valyrian steel swords of Westeros despite not being a Valyrian sword.
House Jordayne ruled as Kings of Tor and at one point, forced House Martell into submission. They were eventually subdued presumably by House Yronwood, who in turn were subdued by House Nymeros-Martell. They are today major vassals to House Martell.
House Fowler reigned as Kings of Stone and Sky. At height of their power, they attempted an invasion of Reach which was repulsed by King Garth VII Gardener of High Garden. They were subdued by House Martell (Officially Nymeros-Martell) after Princess Nymeria of Rhoynar landed in Dorne and forged a marital alliance with House Martell. Last of their Kings was Garrison Fowler who was sent to the wall by Nymeria. They are major vassals to House Martell today.
House Manwoody ruled as Kings in the early days. They were subdued by House Martell (Officially Nymeros-Martell) after Princess Nymeria of Rhoynar landed in Dorne and forged a marital alliance with House Martell. Last of their Kings was Albin Mandwoody who was sent to the wall by Nymeria. They are major vassals to House Martell today.
House Yronwood, the Bloodroyals, ruled over greater half of Dorne. They often vied for dominance with Storm Kings, Martells and Reachmen. When Princess Nymeria landed and married Mors Martell, initiating a war of subjugation, Yronwoods proved to be the fiercest opponents. King Yorick V Yronwood personally slew Prince Mors Martell, leaving Nymeria a widow and guardian of her children with the Prince. After 11 years of bitter fighting, Martells prevailed and Nymeria sent Yorick Yronwood to the Wall. They are today major vassals to House Martell.
There is also this absurd union of different minor Houses who used to elect a self-proclaimed "High King of Dorne" but I haven't added them to keep things from getting way out of hand (They have already gotten out of hand :P, I may add them in future.)
I'll end this answer with "Sic transit gloria mundi".
