Which Bowie songs would you show someone to make him/her love Bowie's music?

Ooh, I like this question.

Naturally, it depends on the circumstances, but if they were just your average person (into mainly mainstream music), then I would begin by attempting to see how familiar they already are (subconsciously) with Bowie, as most people have heard at least a cover of one of his songs.

to do this, I'd probably pay them 'Changes,' as it made an appearance (feat. some other singer) in one of the Shreck films, which my friends would have seen. I would then impress upon them the diversity of his voice and music, so that they would not base their oppinion on him off that one song.
To lay good foundations for their inevitable Bowie idolisation, they would need to hear snippets from all his CDs and images from all his periods, but fistly, they must become aquainted with that which others know of him: the mainstream Bowie. To do this (with a little extra awesome), they would need to progress from "The Best of Bowie" to The Platinum Collection, which would go a ways to covering all bases, but not quite completely. If they'd managed to sit through all of that, they are probably already enamoured with Bowie, but, supposing that they are merely bored, you must then wow them with your favourite track from each of his albums.

But if I had to reccommend just one song, not a whole schema, it would probably be "Rock 'n' Roll With Me,' because it encapsulates the more acceptable and mainstream side of things, with its singable chorus and simple nature, whilst still hinting at his more 'interesting' side, with his Ziggy-esque intonage and overall showiness.

Overall, if someone is going to love Bowie's music, they must have heard his hits, as well as some lesser-known songs, so that they can acknowledge all aspects of his music are to their liking, and proceed accordingly.
Must-hears are obviously Space Oddity, Ziggy Stardust, Changes, Under Pressure (w. Queen), annnd Life On Mars?

- Was this as advice to you or just interest in how well we're all converting our friend to Bowieism? :D

Well, the first song of Bowie I ever heard was 'Changes', and I immediately fell in love with him, but maybe, as my friends are mostly silly teen girls, I'd start with something more direct, like Ziggy Stardust or Moonage Daydream.
Then I'd show him/her this photo, and make sure he/she doesn't drool on it.
This is: 'Bowiefan in ten minutes', bye :)

Something from his Ziggy Stardust period or from "Diamond Dogs"

I showed my younger brother the space oddity video. After it was over he walked to my computer and started transfering my bowie discography to his ipod :)

When i play someone my favourite songs i try to show them videos and pictures at the same time. It makes the songs more memorable for them that way.

Wild is the wind
I'm afraid of americans (^_^)
Kooks
&
Ziggy Stardust! Yay! ^_^

china girl

It depend of the person but for someone more into pop music, "Oh You Pretty Things" with this catchy melody it's just perfect! And for rock-addict I would say "The Man Who Sold The World", mostly because of the (good) Nirvana cover.
I should add that this songs were tasted by my own friends who now looove Bowie!