In Tolkien's universe, Eru represents the one God while the Valar are described as "the powers of the world".
We are told that some Men worship the Valar, mistaking them for gods (a reference to pagan gods, I believe).
What was the relationship between the different elvish factions and the Valar? Did any elves worship them as gods?
In fact there's very little worship among elves at all. This is discussed somewhat in Letter 153; Tolkien likens the relationship to a Catholic calling on a saint:
There are thus no temples or 'churches' or fanes in this 'world' among 'good' peoples. They had little or no 'religion' in the sense of worship. For help they may call on a Vala (as Elbereth), as a Catholic might on a Saint, though no doubt knowing in theory as well as he that the power of the Vala was limited and derivative. But this is a 'primitive age': and these folk may be said to view the Valar as children view their parents or immediate adult superiors, and though they know they are subjects of the King he does not live in their country nor have there any dwelling.
The Letters of J.R.R. Tolkien 153: To Peter Hastings (draft). September 1954
Earlier in the letter, he again remarks that the Valar are to be revered, not worshipped:
The immediate 'authorities' are the Valar (the Powers or Authorities): the 'gods'. But they are only created spirits – of high angelic order we should say, with their attendant lesser angels – reverend, therefore, but not worshipful
The Letters of J.R.R. Tolkien 153: To Peter Hastings (draft). September 1954
That being said, it's not impossible that certain elvish sects, like the Avari, did practice worship of the Valar; but so little is written about them that we can't say for certain.
The Valaquenta (part of the Silmarillion) gives some clues about Elvish attitudes toward the Valar.
Of all the Great Ones who dwell in this world the Elves hold Varda most in reverence and love. Elbereth they name her, and they call upon her name out of the shadows of Middle-earth, and uplift it in song at the rising of the stars.
"The Silmarillion", first American edition pg. 26
"Reverence" and "Love" definitely hold some religious connotations, but aren't as strong as "worship". In light of the fact that elves had direct relationships with the Valar from the time that they first awakened, it seems likely that elves viewed them as teachers and protectors (albeit ones immeasurably greater than themselves) rather than gods.
In contrast, humans only know about the Valar through mythology, which lead to deification.
