Money makes the Wizarding World go round, even if magic helps. Transfiguration and conjuration may be included in Hogwart's curriculum, but it's still impossible to get by in the Wizarding World without some galleons, sickles, and knuts. After all, not every problem can be solved with an Unforgivable Curse.
While Harry Potter had a vault full of gold waiting for him when he began his magical studies, Tom Riddle was plucked from an orphanage without any money or possessions. When it came time for him to pursue his dreams of tyrannical pure-blood supremacy, it's most likely he relied on these devout followers to fund his conquests for power.
Crabbe and Goyle Sr.
Much like their sons, Crabbe Sr. and Goyle Sr. are not particularly smart or powerful. They're present at Little Hangleton Graveyard and The Battle of the Department of Mysteries, but it's clear that they are little more than grunts among the Death Eater ranks.
Despite being portrayed as relatively unintelligent, they somehow are acquitted of their crimes following the First Wizarding War. The money amassed by their extensive pure-blood lineage was likely the only thing that kept them out of Azkaban and in Voldemort's good graces after he regains power.
Nott
Nott started as a simple member of Tom Riddle's Hogwarts gang and eventually became one of Voldemort's first Death Eaters. Just like Crabbe and Goyle Sr., Nott came from old pure-blood money and narrowly avoided Azkaban in the wake of Voldemort's original demise. It seems that those sorted in Slytherin are just predestined to be villains, although there are plenty of villainous acts completed by those in Gryffindor as well.
When the Dark Lord returns, Nott is there to proclaim himself to be his "most faithful servant", yet he is scarcely seen on the front lines after that. If Nott truly considers himself to be a Bellatrix Lestrange level Death Eater, then he must be kicking in an awful lot of coin for creepy masks.
Igor Karkaroff
Arrested by Alastor Moody and sent to Azkaban for his crimes, Igor Karkaroff is eventually released in exchange for the names of his fellow Death Eaters. In spite of his crimes, Igor goes on to become the Headmaster of the Durmstrang Institute.
Much like the Headmasters of Hogwarts, this position presumably brings with it a great deal of power, influence, and wealth. Had he decided to return to his Death Eater activities, he could have been a powerful ally in the Second Wizarding World. Instead, he was executed by his former compatriots for his betrayal.
Dolores Umbridge
Despite being born a poor half-blood witch, Dolores Umbridge works tirelessly throughout her career to hide all knowledge of her upbringing, and prosecute those who share her blood status. Part of this is her expert use of lies, gaudy old rings, and even Salazar Slytherin's evil Horcrux-containing locket to trick those around her into thinking she's more important than she really is.
While she tries to act as if she is one of the wealthiest Dark Witches, the reality is that her time at the ministry did not gain her as much wealth as she desires. She's also not technically a Death Eater - however, she has enough power and does enough terrible things in support of Dark ideals that she can almost be an honorary Death Eater.
Barty Crouch Jr.
While Barty Crouch Sr. dedicated his life to defeating the Death Eater menace during the First Wizarding War, Barty Crouch Jr. dedicated his life to keeping it alive. Without the latter, it's likely the Second Wizarding War wouldn't have happened at all. He ultimately receives the dementor's kiss, but Barty's sacrifice allows Voldemort to return.
Other than Bellatrix, Barty Jr. appears to be the most devoted of the Dark Lord's followers, willing to go to any lengths to achieve his goals. And given his family connections, presumably he has access to a lot of family gold to do so.
Regulus Black
Regulus Black, the younger brother of Sirius, was a Death Eater during the First Wizarding War. He idolized Voldemort and received his dark mark at the ripe age of 16. He was fully supported by his parents, Orion and Walburga, who believed that Voldemort's cause was a righteous one, although they never officially joined his ranks themselves.
Being among the most powerful families in the Wizarding World, Regulus and House Black was undoubtedly a valuable addition to the Death Eater militia. Unfortunately, this addition culminates in Regulus stealing a Horcrux and his untimely death at only 18 - so his wealth always remained family money, rather than specifically his.
Lucius Malfoy
Another Death Eater with a storied pure-blood lineage, Lucius Malfoy served as Voldemort's second-in-command during the First Wizarding War and promptly returned to the Dark Lord's side when he returned. Lucius certainly has a case to be considered the richest Death Eater, but by the end of the Second Wizarding War, it appears that Voldemort has stolen nearly everything from the man.
The Minsitry strips his manor of Dark objects, Voldemort takes over, and Lucius is left a shadow of his former self. With his wealth evaporated and his capability doubted, he was relegated to being little more than Voldemort's whipping boy. No surprise considering that his master plan to open the Chamber of Secrets was spoiled by Harry at age 12.
Narcissa Malfoy
Lucius may get more attention, but Narcissa played a much more pivotal role in the outcome of the Wizarding War. She stopped short of ever being a full-fledged Death Eater, choosing instead to always keep her true alliance to her family.
Before being married to Lucius, Narcissa Malfoy was a member of the Black Family and likely only married into the Malfoy family to expand her wealth, influence, and to progress her pure-blood beliefs. With access to both Malfoy and Black family resources, it's safe to say that Narcissa wielded as much, if not more, influence than her husband.
Bellatrix Lestrange
Gringotts Wizarding Bank is home to countless vaults full of treasures and artifacts, most of which will forever remain a mystery. One of the few vaults that have been opened is the one belonging to Bellatrix Lestrange, and it is packed to the brim with treasures galore. Not surprising given her family's status as one of the oldest bloodlines in the Wizarding World.
Assuming she didn't ruin all that treasure with a curse to protect Helga Hufflepuff's Cup, the Lestrange Vault is likely among the most valuable in the bank, let alone among Death Eaters. Bellatrix's wealth is only matched by the horrible acts she commits throughout the war.
Delphini
Despite her marriage to Rodolphus Lestrange, Bellatrix Lestrange conceived a child with the Dark Lord sometime during the Second Wizarding War. This child, Delphini, goes on to become the last living heir of Salazar Slytherin, the last in the line of Lestrange, and a witch of considerable power.
Assuming estates function in the Wizarding World as they do the Muggle World, Delphini would appear to be the sole heir to Voldemort and Bellatrix's possessions, in addition to having some claim to the Black fortune. This combo of strength, cunning, and ancient family wealth nearly lead to Voldemort's return and a new world order.