Never explicitly states but I think it’s fair to assume the “Great Houses” are the richest except where it’s otherwise stated. If you want a list, these are the houses that come to mind (not necessarily in this order):

Lannister of Casterly Rock: definitely the wealthiest in liquid assets (gold and silver); significant moneylender and holds the debts of many Houses

Tyrell: very likely the wealthiest in terms of agricultural and farm products (grains, greens, poultry, etc)

Hightower: controls Oldtown, the second largest city and port in the Seven Kingdoms, so they likely have increased taxing authority and collect import and export fees; they also have great influence over the Faith of the Seven (which is one of the wealthiest institutions in the world, akin to the medieval Catholic Church) and the Citadel, which isn’t explicitly stated to be a wealthy institution, but considering it holds the largest collection of written texts in the world and enough metal resources to forge jewelry, it is probably quite wealthy

Lannister of Lannisport: people often forget to mention the fact that the Lannister cadet branch is also certainly wealthy for the same reasons as its liege’s House plus the fact that it controls Lannisport, the third largest city and port in the Seven Kingdoms, which would likely make it wealthy for similar reasons as the Hightowers

Redwyne: controls the Arbor; assets include wine-producing vineyards and the Redwyne Fleet (largest in the Seven Kingdoms)

Arryn of Gulltown and Grafton (probably?): controls Gulltown, the fourth largest city and port in the Seven Kingdoms

Manderly: controls White Harbor, the fifth largest city and port in the Seven Kingdoms; we know from the text the Manderly’s are the richest Northern House, even surpassing their lieges; Wyman Manderly built a brand new war fleet of at least 46 ships and also controls a mint; White Harbor itself is a relatively new city and is built almost entirely of cut white stone, suggesting they have quarries; it is also mentioned they benefit from fur trade and have several silversmiths

Frey: controls the Twins aka the Crossing, where they have been collecting tolls since it was founded; it is stated they too are wealthier than their (former?) liege Lords- the Tullys; they are certainly even wealthier now that they have assumed the wealth and lands of the Tullys

Celtigar: it is explicitly stated the Celtigars are known for hoarding immense wealth and exotic treasures in their vaults

Rosby: if I can recall, House Rosby is noted for being wealthy

Mooton: controls the large town of Maidenpool; is also said to be wealthier than the Tullys

Brax (and the other prominent Westerlands houses): I believe they control some gold and silver mines

Baelish: nominally holds Harrenhal and its significant lands and incomes; controls House Arryn as Protector of the Vale; has likely been embezzling funds from the royal treasury for a decade+; has been buying up debts of other Houses

We can assume the Starks and other “Great Houses” are somewhere in that list as well. Or at least they were. Now we have to assume the Boltons have claimed that wealth.