If we had unlimited resources of all kinds; food, shelter, land, luxury goods, etc. then we wouldn't have nor need money; money is just an abstract representation of limited resources.
We're competitive by nature, however, so I don't think that'd go away right away, but we'd probably favor peaceful competitions like sports, games, judging contests and pageants for various things, much like we do today, but absent the need to struggle those would probably take a greater prominence in our lives.
Art, science, scholarship, and philosophy would also probably become much more important, as we'd have the time to contemplate ourselves and the universe around us without survival pressures. The human thirst to learn, grow, and improve wouldn't die out. In fact, it may very well be set free for the first time in human history.