Checking in early might get a sympathetic agent who can put you on an earlier flight. As said previously, they do not have to do it, but I believe there have been comments previously where this has happened. I'd also suggest there is a very good chance of being put on an earlier flight if the agent can see delays in they system or if there is bad weather.

The 60 minute rule might work for some, but it doesn't reflect reality IMHO for low stress travel.