I've worked with CakePHP and Django and I really recommend Django. I don't know too much about CodeIgniter, but I remember ruling it out when I was evaluating frameworks myself about a year ago. CakePHP seemed much more developed at the time.
First of all, the Django community is much bigger and has spent a lot of time focusing on reusable apps. This means that you get a lot of functionality for free. Pair this with the django admin, and you have a lot of things already done for you. I haven't kept up with the PHP frameworks much, but I'm pretty sure Django is also more developed.
This is more of a personal thing, but I just like Python over PHP. Compare the way models are done in CakePHP and Django: http://book.cakephp.org/view/67/Understanding-Models, http://docs.djangoproject.com/en/dev/topics/db/models/#topics-db-models. The python is clearly more readable.
Keep in mind that Django gives you an awesome ORM and builds your schema for you, i.e. you never have to touch the database if you don't want to. With the PHP frameworks, you have to do your own db design, which just slows me down at this point. You can always go in and add indexes for speed later.
This is probably the most biased, but if you are starting a new application - seriously - just stick with Django or Ruby on Rails. There is a reason everyone talks about them and they have the biggest communities and best developers behind them.
You can also check out Pinax for a lot of Django goodies.