The short answer is that they did, both in the form of New Orleans Voodoo (separate from its Haitian cousin) and in the folk practices collectively called "Hoodoo," "Root Work," "Conjure," or "Spirit Work."

Most of the complex of beliefs called Hoodoo (or whichever name) was really decentralized, though, mostly because of differences in the way the United States treated slaves - though I think it's also a reflection of Protestantism (most denominations having a decentralized authority) as opposed to the centralized structure of Catholicism, the dominant religion in Haiti, Cuba and Brazil.

Because of this decentralization, studying Hoodoo has been more like folklore studies than religious anthropology. I'm not really aware of much formal scholarship earlier than Hazzard-Donald's Mojo Workin'... but lots of informal or "interested amateur" stuff, like Cat Yronwode's "Lucky Mojo" writings. Yronwode is pretty thorough, but is also in the business of selling things, so, you know.

You can see traces of Hoodoo practices in all kinds of things, from references to "John Conqueroo" in old blues songs (actually "St. John-the-Conqueror root", another name for lesser galangal) to the spells the kids argue over in Tom Sawyer:

"Say -- what is dead cats good for, Huck?"

"Good for? Cure warts with."

"No! Is that so? I know something that's better."

"I bet you don't. What is it?"

"Why, spunk-water."

"Spunk-water! I wouldn't give a dern for spunk-water."

"You wouldn't, wouldn't you? D'you ever try it?"

"No, I hain't. But Bob Tanner did."

"Who told you so!"

"Why, he told Jeff Thatcher, and Jeff told Johnny Baker, and Johnny told Jim Hollis, and Jim told Ben Rogers, and Ben told a n****r, and the n****r told me. There now!"

"Well, what of it? They'll all lie. Leastways all but the n****r. I don't know him. But I never see a n****r that wouldn't lie. Shucks! Now you tell me how Bob Tanner done it, Huck."

"Why, he took and dipped his hand in a rotten stump where the rain-water was."

"In the daytime?"

"Certainly."

"With his face to the stump?"

"Yes. Least I reckon so."

"Did he say anything?"

"I don't reckon he did. I don't know."

"Aha! Talk about trying to cure warts with spunk-water such a blame fool way as that! Why, that ain't a-going to do any good. You got to go all by yourself, to the middle of the woods, where you know there's a spunk-water stump, and just as it's midnight you back up against the stump and jam your hand in and say:

'Barley-corn, barley-corn, injun-meal shorts, Spunk-water, spunk-water, swaller these warts,'

and then walk away quick, eleven steps, with your eyes shut, and then turn around three times and walk home without speaking to anybody. Because if you speak the charm's busted."

"Well, that sounds like a good way; but that ain't the way Bob Tanner done."

There's a rich spiritual tradition behind the little charms and superstitions, but it wasn't unified by institutions like the societies in New Orleans or Cuba, and wasn't so much written down as handed along. Some of the key texts in American Hoodoo were actually grimoires of Jewish - or pseudo-Jewish - magic... you can kind of see the relationship to mainstream religion there, taking "the stuff that works" away from the liturgies and sermons.

EDIT: Can't forget Zora Neale Hurston's early work with hoodoo-as-folklore, although it crosses into Voodoo.

As grantimatter pointed, syncretic beliefs and practices did develop, but there a couple factors as to why those beliefs and practices didn't develop quite like in other countries.

To start, the US never really developed a slave society. A slave society is a society in which slave labor dominates the economic and social hierarchy of a place; where enslaved people make up 90% of the population and rest being free people involved in some way in that slave system. Slave societies developed in other parts of the Americas like many Caribbean islands and parts of Brazil, but didn't develop in the US, with the possible exception of coastal South Carolina (think Gullah/Geechee culture) and the Mississippi Delta. So unlike many slaves in other parts of the Americas, US slaves had more exposure to and interaction with non-enslaved Africans and their beliefs and practices.

The US also had a fairly diverse population of enslaved Africans. About 250,000 enslaved Africans were brought to the US out of 10,000,000 to 20,000,000 total enslaved Africans brought to the Americas. In the early days, many slaves were taken from the Angola and Congo regions but as time went on, slaves began more and more from West Africa. It's important to remember that Africans have very very diverse beliefs and practices. Some early enslaved Africans might have already been Christianized and some enslaved Africans were Muslim. The biggest slave revolt in Brazil was perpetuated by Muslim slaves. Synretic beliefs and practiced developed when many enslaved Africans (and their descendants) shared similar cultural and religious backgrounds. For example Candomble developed from traditional Yoruba beliefs and practices and Voodoo from traditional beliefs practiced in Benin and Togo. Enslaved Africans from different parts of Africa might have little in common. The US also depended more on the natural increase (births) of slaves than other places like Brazil to grow the enslaved population. Meaning that there wasn't a large constant inflow of Africans (and their beliefs and practices) like there was in Brazil.

The US also was predominately Protestant and was going through a couple "Great Awakenings" during the period of slavery. So the idea of spreading a "pure" and true version of Protestant Christianity was very much en vogue amongst many slave owners during this time. A prominent example of this would be Phillis Wheatley who was born in West Africa but become a devout follower of Christianity during the First Great Awakening. In Brazil, the conversion of enslaved Africans was just a formality and slave owners didn't care what slaves actually continued to believe or do. The exception being Islam among slaves due to their relatively rebellious nature.

So in summary, syncretic beliefs and practices did become established among slaves in the US, but it wasn't quite to the extent in other places. This was due to the US not being a slave society, a relatively small and diverse population of enslaved Africans, and Protestant revivalism.