Even if Saeïdryl already find the answer, it also could have been
The One Ring, from The Lord of the Ring
Sweet dreams are made of me,
Ok, that's not what we typically call "sweet dreams" but wearing the One Ring make you see the world like ethereal.
Who am I, that's the question,
I travel the hands,
The One Ring passed from hand to hand : Sauron, Isildur, Déagol...
and the pockets,
"What have I got in my pocket ?" ~ Bilbo Baggins
I can sometimes be immaterial
A mortal wearing the One Ring become invisible. The Ring also become invisible.
Some of them want to trade me
Sméagol tried to get the One Ring from Déagol arguing that it was its birthday... That's some kind of trade...
Some of them want to be traded with me
Ok, that's a little bit far-fetched but if you consider the One Ring's fire inscription, it say :
"One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them."
So we can kind of consider that all the other rings are some kind of extension of the One Ring.
So the nine mortal men have "trade their soul" in exchange of a part of the One Ring power...
Some of them want to play me
Playing the riddles game with Gollum, Bilbo's last question is about the ring. It's like he is playing his final ace.
Some of them even want to flip me
Frodo's big question is whether or not will he be able to "flip" the Ring into the lava like he would have done with a coin... Or will he fail like Isildur ?