Express: How to pass app-instance to routes from a different file?

Node.js supports circular dependencies.
Making use of circular dependencies instead of require('./routes')(app) cleans up a lot of code and makes each module less interdependent on its loading file:

---

app.js

var app = module.exports = express(); //now app.js can be required to bring app into any file

//some app/middleware setup, etc, including 
app.use(app.router);

require('./routes'); //module.exports must be defined before this line

---

routes/index.js

var app = require('../app');

app.get('/', function(req, res, next) {
  res.render('index');
});

//require in some other route files...each of which requires app independently
require('./user');
require('./blog');

---

-----04/2014 update-----
Express 4.0 fixed the usecase for defining routes by adding an express.router() method!
documentation - http://expressjs.com/4x/api.html#router

Example from their new generator:
Writing the route:
https://github.com/expressjs/generator/blob/master/templates/js/routes/index.js
Adding/namespacing it to the app: https://github.com/expressjs/generator/blob/master/templates/js/app.js#L24

There are still usecases for accessing app from other resources, so circular dependencies are still a valid solution.

Use req.app, req.app.get('somekey')

The application variable created by calling express() is set on the request and response objects.

See: https://github.com/visionmedia/express/blob/76147c78a15904d4e4e469095a29d1bec9775ab6/lib/express.js#L34-L35

Like I said in the comments, you can use a function as module.exports. A function is also an object, so you don't have to change your syntax.

app.js

var controllers = require('./controllers')({app: app});

controllers.js

module.exports = function(params)
{
    return require('controllers/index')(params);
}

controllers/index.js

function controllers(params)
{
  var app = params.app;

  controllers.posts = require('./posts');

  controllers.index = function(req, res) {
    // code
  };
}

module.exports = controllers;