Do goldfish need an oxygen machine?

Of course they do! They can't live if they don't! I have 2 goldfishes which live in separate tanks, and theres only 1 oxygen machine,and we only used it on 1 goldfish, and then the other died!! So yes, they do need it!!

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ANOTHER ANSWER

the important thing is that there is oxygen in the water. i achieved this by digging a half metre deep pond in the garden (hoping this is deep enough to not completely freeze in our winters), covering with tarpaulin (you're supposed to have a carpet underlay and overlay to stop the plastic photo-degrading and make it last for years). i filled it with tap water and left it a couple of days to let the fluorine evaporate. then i went to my local pond and got lots of completely submerged plants to oxygenate the water for a week. i also added floating water plants from the pond to provide some cover from sunlight in areas and some marginals with roots in the water to plant round the edges to provide protection and stagnant water for insect larvae which the goldfish feed on. i added lots of pond water-snails to eat dead leaves which have formed a mulch. i bought some shrimp to breed in the pond for food too. i added the goldfish by leaving their bag in the water for an hour before opening it so they could acclimatise to the temperature. one week later and 5 of my 6 baby goldfish look healthy; they have perky sticky-outy fins, swim quickly and are growing much more quickly than i thought they would, their gills are not moving too fast and they are not gulping oxygen from the surface of the water. one looks floppy and lethargic at the bottom of the pond. (aside on my injured fish: i mistakenly poured the fish out of the bag into the pond, leaving one fish trapped and struggling in the plastic in the bag without any water for a second. i think fish injure easily and should have put the opened bag in the water and let the fish swim out. blood-worms from the pet shop have made short work of the dead carcass and my now larger goldfish eat them ravenously, though i really should have quarantined the injured fish. the excess of plants absorbing nitrates and plant cover not allowing much sunlight into the water mean the pond is still clear and i have no algae, though i suppose algae would oxygenate the water too. i find green water unsightly and like to watch the fish.)