Adding a few more comments to this arguement:
If you have a 1000mAhr battery and you take 1mA out of it, it should theoretically last for 1000 hours.
Likewise if you take 10mA out of it, it should last 100 hours.
However, generally as the previous posters have said, if you take 10mA out, the life will be somewhat less than 100 hours. The higher the load current, the more your mAhr rating should be reduced.
The numbers above are just to make the sums easy. Look at the manufacturers datasheet as they have lifetime curves of constant resistance and constant current loads.
In addition, the battery will have a certain amount of self discharge. If you put a battery in an appliance, do all the calcs and come back in 10 years time, your battery will probably be flat, regardless of load. this will be due to self discharge. Generally this is not an issue though.
If you need 10 years life, Lithium Thionyl Chloride batteries are about the best you can get.
Hope this helps..