So, after I created my question, I got this related list on the right with a similar issue: Organize routes in Node.js.
The answer in that post linked to the Express repo on GitHub and suggests to look at the 'route-separation' example.
This helped me change my code, and I now have it working. - Thanks for your comments.
My implementation ended up looking like this;
I require my routes in the app.js:
var express = require('express')
, site = require('./site')
, wiki = require('./wiki');
And I add my routes like this:
app.get('/', site.index);
app.get('/wiki/:id', wiki.show);
app.get('/wiki/:id/edit', wiki.edit);
I have two files called wiki.js and site.js in the root of my app, containing this:
exports.edit = function(req, res) {
var wiki_entry = req.params.id;
res.render('wiki/edit', {
title: 'Editing Wiki',
wiki: wiki_entry
})
}