I've traveled on a container ship before as a legal passenger and Dameon is right - it is very expensive for what you get (room and board). On the other hand, it's a pretty unique form of travel and well worth it if you have the cash.
One thing that i think would be extremely difficult to do is sneaking in and out of container ports. The ships float around in the harbor for ages, then go in to dock for the shortest amount of time possible. Container ports are massive, and heavily patrolled. The containers load and unload remarkably quickly. It'd be tough to get up the gangplank because it's guarded full-time, and riding a container - unless you're inside - would be virtually impossible to do without being seen. You may also land 6 containers up and then you're screwed.
I wonder if one way to do it would be to sail out in a dinghy to international waters and get "rescued" by a crew en route, but that would be so much effort and paperwork i imagine you'd be better off just sailing to your destination yourself.
If you did manage to make it on the ship undetected, i think you could probably sneak about okay. They are very large and there are a bunch of places to hide. The ship i was on had a half court for basketball out the back, which i never saw in use. The crew is always on patrol and cleaning, but i suppose you could figure out the roster if you had a good hiding spot and the time. Maybe hanging out in a life raft would be a good spot, as long as you got out during drills and inspections.