I've seen several instances where people have demonstrated the ease with which encrypted cookies can replace sessions within PHP. Michael Nitschinger wrote a piece recently demonstrating the switch with Lithium, while CodeIgniter does this by default (optionally encrypting). The problem is that while replacing sessions with cookies works, it introduces a few risks not present with native session support, and these risks tend to be under documented.

He gives an illustration of an attacker who sits between Amazon and one of their warehouses. Despite encrypting their order details, all it would take is the attacker to grab an order and copy it and resend (a "replay attack"). He's created an example application to illustrate the point (source on github). The attacker doesn't even have to know what the encrypted information contains - they only have to replicate it.