Vow of Poverty, even if it required no feats and was merely an option freely available to your character, would still take away more than it grants. You can literally buy very-nearly everything Vow of Poverty has to offer, and have hundreds of thousands of gold pieces left over. The only things it has that are legitimately difficult to get are the ability score bonuses (though they are partially replaced by Enhancement bonuses that a Vow of Poverty character has a hard time getting in any permanent fashion), and the extra Exalted feats (the majority of which are very weak).
Vow of Poverty is so bad that if you handed me a character who had already wasted two feats on Sacred Vow and Vow of Poverty, I would break that vow, take my money, and accept that I had two wasted feats slots. It’s that bad.
Magic is, in short, everything in 3.x. It utterly dominates the game. The spellcasters are the most powerful classes, and those who have no innate magic must hunt desperately for the most potent and cost-efficient magical items to overcome that shortcoming.
As such, Vow of Poverty is least bad on the most powerful classes: they can afford to lose their magical items. They’re still better with them than without them – and by the way, one of those things you explicitly cannot have is a Holy Symbol. Yes, this means you cannot make a Cleric with Vow of Poverty. Yes, this is very, very dumb. Wizards have an even bigger problem, in that they can’t have a Spellbook. (There are ways around these problems, options that might even be good if you’re not using Vow of Poverty, but they are not reasons to take Vow of Poverty.)
Particularly if Wildling Clasps are not available, a Druid may not make extensive use of magic items. Therefore, the Druid – spending most of his time in Wild Shape anyway – is the best candidate for Vow of Poverty. You can still do more with magic items than you can do with Vow of Poverty, even with a Druid, even without Wildling Clasps, however. You will also note that the Druid is one of the five most powerful classes in the game, and almost certainly the most-obviously overpowered of the bunch. It’s fairly easy to miss what makes a Cleric or Wizard so powerful. It’s not hard to figure out that being a bear with a pet bear who shoots more bears is awesome and terrifying.
Totemists and Incarnates, from Magic of Incarnum, fall in a somewhat similar boat: their class features replace magic items to a certain degree. Not totally, but enough that they generally use somewhat fewer of them than most other classes. It’s still a really bad choice though: at very-low levels, they don’t get many Chakra Binds that are replacing magic item slots, so they can use items normally, and at high levels the sheer amount of wealth they’re losing makes Vow of Poverty a non-starter.
Psionic manifesters, being magic classes that don’t rely on foci or components or things, can at least continue to do their main schtick while taking a Vow of Poverty. Again, though, there are plenty of magic/psionic items that are worth way, way more to them than the bonuses from Vow of Poverty are.
For a nonmagic class, there isn’t even a discussion. Mid-to-high level 3.5 requires all kinds of things that they do not get natively, and Vow of Poverty will never grant them. This includes Flight, dealing with a variety of Damage Reductions, dealing with Miss Chances, finding ways of Teleporting, finding immunities against terrible things like [Death], [Mind-Affecting], and the smorgasbord of things freedom of movement protects you against.
Monks, one of the most touted ascetics out there, are a particularly bad case. The Monk is a very weak class, and needs a huge array of things just to keep up. A Necklace of Natural Attacks is literally part of the cost of entry. A Fanged Ring is something you’ll really, really miss. Magic items that will make you larger are simply invaluable. All those aforementioned things to deal with apply to the Monk too. And so on.
The only conceivable exception to the rule that Vow of Poverty makes a character worse is the Apostle of Peace, an incredibly broken prestige class from the Book of Exalted Deeds. It’s not that the Vow’s bonuses somehow magically synergize with the class in some amazing way – that is, it’s nothing good about the Vow itself. It’s simply that Apostle of Peace requires that you have it. The Apostle of Peace, however, is one of the worst classes in the game, not simply because it’s overpowered (which it is), but because it also literally breaks almost all of the game’s assumptions.
Using Vow of Poverty to become a “Tank”
Zach’s answer suggests that Vow of Poverty can make a character “indestructable.” It cannot do any such thing. High AC, high saves, yes. Indestructable, not even close.
Moreover, even if it did, this would be a failing tactic anyway. Intelligent enemies will simply ignore the non-threat and kill his party. Since he's got no damage output, there is nothing he can do about it. Unless there’s a choke-point he can hold (and the enemy has no alternate ways around him, like Teleporting), they’ll just go around him and attack the real threats.
And even if it were a good idea, you can achieve higher AC without Vow of Poverty than you can with it. And you can certainly be much closer to indestructable (at high-optimization and high level, basically every Tier-1 spellcaster already is).