[Garen LiLorian]

Edit; Whoops, cross-posted with Elianna
The character who leaps to my mind for this archtype is Bombadil,

an elemental, whimsical being, whose integration into human society is only partial. There is a dichotomy in his nature, which prevents his ever breaking entirely free of his chaotic, primordial mould.

This fits pretty well.

He knows neither good nor evil yet he is responsible for both.

This is also represented in the text, though it is a little less obvious. It is obvious that he is responsible for good, through helping the hobbits, however at the council of Elrond Gandalf says he would not take the ring

"...willingly. He might do so, if all the free folk of the world begged him, but he would not understand the need. And if he were given the Ring, he would soon forget it, or most likely throw it away."

This seems to indicate he has no knowledge (or care, which is probably a better way of putting it) for 'good' or 'evil' as the outside world defines them. It could also be stated that he is responsible for evil, as he is Master of the Old Forest, an area feared as evil by the Hobbits.

Several of the Trickster's defining qualities

"At times, he is constrained to behave as he does from impulses over which he has no control," " is at the mercy of his passions and appetites" "a malignant tease"

are noticably missing from Bombadil, however. They show up quite nicely in Gollum, however, as Encaitare points out. Gollum also has the whole "responsible for both good and evil" thing going, although I wouldn't agree with the case that he doesn't know them. I also agree with Enca that Gollum doesn't count as a culture hero, though I guess that one's open to debate. In the context of LotR as a myth, Gollum has a pretty good hold on a trickster archtype. However, in the context of Middle-Earth itself, I still like Bombadil.

In the end, although Bombadil has many aspects of the Trickster, he is clearly a cleaned-up one. This makes some element of sense, as Tolkien's world is quite a bit more (can't quite find the right word...) socially acceptable than the sex-and-gore world that the Trickster largely inhabits in various cultural mythologies. Tolkien also (at least in LotR) takes some pains to delineate the boundary between good and evil, and someone so ambiguous as the Trickster archtype could not reasonably exist in all his full glory in the context of LotR. (IMHO, at least)