If you're asking which songs are easy, that generally depends on your vocal range. You should probably avoid Changes, Life on Mars?, and Starman. Space Oddity is hit or miss - sometimes the crowd gets with you and drowns out the parts you struggle with, sometimes they don't.
If you're going for crowd reaction, general karaoke rules apply. People respond well to performers who dance and/or are loud; people respond well to songs that they can dance to or be wail along with. On that front:
Young Americans: Dance you monkey bastard! Young Americans is a more difficult song than it appears at face value, both due to dramatic changes in pitch and the wearing-out effect of its pretty much relentless vocals. If you watch Bowie's live performances, you can really see this: He generally drops the high points back in line with the rest of the song (even "break down and cry!", excepting when he lengthens the pause - not an option for karaoke, unfortunately), and his voice really starts wearing thin as the song goes on. Typically the line "look at your hands shake" barely gets croaked out, and you'll understand why if you try to master the song.
Golden Years: Similar case to Young Americans, except less dancy and slightly less well-recognized. Fortunately, also easier. Be sure to meter your output between "one of these days" and "ALL THE WAY!", as it's a lot of lyrics to get through without a breath, and you have to be loud at the end.
Let's Dance: Pretty safe choice, as the crowd will probably know it. Ironically it's kind of hard to dance to, particularly while trying to project some serious-moonlight cool. Fairly easy vocals to deliver, and has some points where you can get loud (remember that, in karaoke, more is more when you get to line like "tremble LIKE A FLOOOOOWWW-ERGH!")
Jump They Say: Fits my vocal range fairly well, so I'm partial to it (plus I just dig the song). One of the more danceable tracks, which makes it work; unfortunately, it's not a song anyone's gonna know, so you will have to sell it to them, and fast.
Rock 'n' Roll Suicide: A middle-ground choice. Unless there are Bowie fans in the room, no one will be paying attention for most of it - but, if you really, really work the loud lyrics at the end, you'll pull them back in.
China Girl: A very strong choice. I have a personal habit of trying to do it in a more Iggy Pop style (which is blown the instant the opening bars come up, but whatever), which confuses people at first, then they begin to enjoy the weird gyrations, then they really start enjoying the yelling of the lines near the end. Performed as Bowie does, I think it would get an overall positive reaction, but I think it would be boring to be the person actually singing it.
Under Pressure: Sigh. This song is a disaster waiting to happen. It needs to be a duet, both people need to know the song very well, specifically which lyrics are sung by which person. To top it off, neither Bowie's nor Mercury's vocal part is anything close to easy. To top it off, despite being recognizable, it's hard to be very animated about. Unless you have it down pat, you will probably just end up irritating people slightly.
Blue Jean: A decent number of people will probably know it, but make sure that you do - you will need a lot of stage presence to pull it off properly. Be intense, and when the time comes, be very loud (the second point, if it's not clear, applies to every song.)
Suffragette City: Move your legs at the pace of this song and people will love it, no matter how badly your vocals are. Also a good song to employ some leg kicks. If you do not feel ready to pass out by the time the song is over, you probably did not try hard enough.
Rebel Rebel: I haven't found a way to make this one work. It's a well-known song, so often you'll get a good reaction just when it comes on; after that though, it's really kind of boring, by karaoke standards. For one thing, it's slower than the attitude of the song suggests. And there's also not much to dance to. Most significantly, it's really repetitive, which means you're apt to get bored up there doing it. What generally happens is sort of a negative feedback loop, where the crowd cools a bit after their initial reaction, and you begin to realize that it's going to be like this pretty much all the way to the end so you start to get anxious to see it end, the crowd picks up on that and starts to share your feelings... I feel like there must be some way to keep that initial moment of interest alive and transform it into a solid performance, but I haven't found it yet.
Ziggy Stardust, Ashes to Ashes: I bomb on these vocally, and they don't offer me much opportunity to save it with silly dancing, so I'm not fond of them. Still, they're well-known enough that you could probably get a decent reaction if you sang them well.
Absolute Beginners, Sorrow, Drive In Saturday, et cetera: People won't know the songs and you won't have many options to bring them in. Save these for moments of pure self-indulgence.
Also, some songs not listed under Bowie that can be done in a Bowie style:
Let's Spend the Night Together: Obviously a bit slower and much steadier than Bowie's cover, but you can still adapt Bowie's vocal inflections to most of the lyrics. Also fairly dance-able. The crowd will like it, but only if you work hard at it; otherwise, it becomes fairly boring.
Alabama Song: Again, slower pace than the Bowie cover (this particular one is available in so many different versions that it may not always be the case, though). Another one that the crowd won't care about, even if you nail it, but sometimes fun all the same. Throw in an "auf wiedersehen" and look around for that spark of recognition - you won't find it.
All the Young Dudes: Can certainly be done in a Bowie style! The Mott version will have a lot of "extra" lyrics showing up on screen, but don't let them throw you off. It is, however, kind of a boring song; I recommend looking at David Live and stealing some of those vocal riffs (although be careful about getting too used to the slower tempo of that version), as those add at least some interest.
Across the Universe: You can throw Bowie-style vocals on top of the Beatles-style instrumentation, but it will still be as agonizingly boring as the Beatles version.
The Man Who Sold the World: Some places have this listed under Nirvana, with instrumentation very like their Unplugged cover. This one comes right back to Bowie if you approach the vocals in that manner. Crowd reaction has also been more positive than I could ever understand, considering this is a non-dance song without a ton of pop appeal.
Hurt: Generally listed under Johnny Cash, I think. Just remember how boring Bowie's version was - yours will probably be worse.
Lust for Life: Hey, music by David Bowie at least. Everyone knows it and people will like it if you are very loud and do not stand still. The Passenger is available in some places but I haven't had occasion to do it; I imagine it would bomb.
My Way: If you're really hardcore, memorize the lyrics for Even a Fool Learns to Love and confuse the fuck out of everyone in the bar.
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