The battery is only covered under defects, and as being a consumable part, is only covered under the first year, APP or not. [[edit: this line removed for inaccuracies]].
After that, as long as there is no serious physical damage or any spill damage ("accidental damage") then every Apple branded part will be replaced. If you add in extra RAM or bigger hard drive, those parts obviously will not be covered by Apple. If you drop your machine and there is no signs of it then you can get parts replaced. If, however, you drop it and there is a huge dent on the corner, but you don't have a problem internally until a year later it will not be covered under APP due to the damage.
Software is not covered, nor is your data. The DVD's included with every machine allow you to reinstall if you have problems, and your data is your data. They can't be held responsible for people too lazy to backup especially with external storage being as cheap as it is these days.
The unofficial/official policy for replacement computers is typically after the third MAJOR repair (which are most parts in the machine) and currently having the 4th major repair. Depending on who you talk to, they will either tell you that they are replacing it or otherwise you will have to suggest that you would like the faulty machine replaced completely. If Apple can't replace the part in a reasonable time (I've seen this happen after 2 weeks with no part from Apple), or they no longer carry the model you have, they can replace it with a newer machine. Apple has sole discretion to whether or not they will replace a machine. I have seen people get their MacBook replaced after the screen scracked, even though that is in no way covered by AppleCare. I've also heard of repairs happening days after the warranty period ended.
There are mistakes made by every warranty service out there for every device with their very own horror stories. However, just like the two stories above there are also many great things that you will most likely never hear about. Of the millions who are satisfied with a product you don't hear about it, however, once someone has a problem you can't get them to shut up (nobody complains about things working perfectly). The relatively few bad stories you hear are in no way a reflection upon AppleCare as a whole.
