Like a used car, it depends on the bike, who owned it, how they maintained it, and how they rode it. My Intruder VS800 has over 20,000 miles on it in four years of use, and it is hardly broken in yet and has never has a single mechanical problem. My friend has 94,000 miles and counting on his Intruder 1500LC, and has never has a problem. People tell me that when you look at a used Gold Wing, don't think twice if it has over 150,000 miles on it. A neighbor is obsessive about keeping his CBR perfect, and has over 15,000 trouble-free miles on it so far.
But on the other hand, I have seen kids absolutely destroy their first sport bike in less than 5,000 miles, by abusing it, riding it too hard, and not doing any maintenance to it. And lets face it, some models of bikes have the reputation for being 'bullet proof', while others should be avoided no matter how few miles they have on them.
So when you look at a used bike, overall condition if more important than miles. Consider who owned it before you: was it an experienced adult rider with a garage who documented the factory-recommended services and changed the oil like he should, or was it some irresponsible, hot dog rookie rider who left it outside, could not afford to bring it in for service, and only changed the oil when the light came on? Can the owner prove they had regular maintenance work done with receipts, or did they just clean the bike up and change the oil last night so they could put it in bike trader today? Do they have a long list of new parts they have put on, indicating that they abused the bike and broke a lot of things? Do the pegs, grips, and fairings (if applicable) show signs of normal wear and tear, or are they shinny new like the bike was dumped and just repaired, and they are trying to unload the bike before it falls apart? Do the tires show normal wear, or are they absolutely brand new, like they were changed yesterday just so you would not see how badly trashed the old set was and know that the owner abused the bike? All these things are more important than mileage, but keep mileage in mind when negotiating the price once you find a good one.