You should look into Freebase (see, for example, their musical artists table).  If you do choose Wikipedia, then you should probably download a database dump.
Example comparing genre listings of Freebase and Wikipedia for the band Radiohead:
- Freebase: alternative rock, art rock, electronic music, progressive rock, electronica, and experimental rock.
 
- Wikipedia: alternative rock, electronic, and experimental rock.
 
Edit: More importantly, I've included a working example using mjt, a Javascript framework designed for Freebase.  Copy-paste this into a file, open with your browser, enter an artist's name, and see which genres Freebase has for them.
Less importantly, I've changed my examples and default to Radiohead.  =)
<html>
<head>
  <script type="text/javascript" src="http://mjtemplate.org/dist/mjt-0.6/mjt.js"></script>
</head>
<body onload="mjt.run()">
<pre mjt.script="">
var name = mjt.urlquery.name ? mjt.urlquery.name : 'Radiohead';
</pre>
<div mjt.task="q">
mjt.freebase.MqlRead([{
  type: '/music/artist',
  name: {
    value:name,
    lang:{name:{value:'English'}}
  },
  genre: [{
    name: {
      value:null,
      lang:{name:{value:'English'}}}
  }]
}])
</div>
<form method="get" action="">
<input type="text" name="name" value="$name" />
<input type="submit" value="search" />
</form>
<table mjt.for="topic in q.result">
  <tr mjt.for="(var rowi = 0; rowi < topic.genre.length; rowi++)">
    <td><pre mjt.script="">var gname = topic.genre[rowi].name;</pre>$gname.value</td>
  </tr>
</table>
</body></html>
You're most likely using another language, but hopefully you can easily translate the above query.