[Mithadan]

An interesting aspect of some of the answers above is the apparent assumption that members of the Fellowship were offered the Ring as the means toward achieving their desires. I do not believe this to be the case. Galadriel's test was geared towards testing the loyalty of each member of the Fellowship by offering something they truly wanted if they turned aside. While I have little doubt that Boromir's heart craved the Ring (and maybe part of the test was to see if the Ring-desire had taken hold of anyone) I do not think that the others were offered the Ring.

Only Sam's "desire" is clearly stated: a hole of his own with a bit of a garden. This is actually rather telling. Because Sam is a servant. He is Frodo's "man" in the British sense. For him to want property ownership of his own is akin to him wanting release from servitude. And, ironically, in the end he gets this.

Merry concedes being offered something similar, but slightly different. He declines to say more. I get the sense that revealing your inner desire is something very personal and that Galadriel, by effectively perceiving it in each member, is invading their privacy in a disturbing way. I almost wonder if this results from an Elf not perceiving what a Man might not like. Nonetheless, I cannot imagine specifically what either Merry or Pippin might want.

I guess that Gimli is easy. As others suggest, he was offered a kingdom of some sort and its attendant riches.

Aragorn is actually interesting. He almost certainly desired Arwen above all else. He could, as someone speculated, have been offered an "easy" way out to this end, somehow. However, I suspect he was presented with the kingship of Gondor as that was the condition of his betrothal to Arwen. How Galadriel might show Aragorn a way to achieve this I do not know. I do not think he would have been offered the Ring.