LI-Ion batteries are only good for about 500 charges (or less). Thus, if you use it on battery every day, and charge at night, you only get 1.5 years. The battery on my thinkpad A21M lasted a year before I noticed degradation, and another year before it was to less then half.
I don't know what the number is for NiMH, but it's higher. But, you don't get the charge density associated with Li-Ion batteries, so they aren't used much in laptops anymore.
All batteries self discharge. Most laptops won't charge the battery unless it falls below a certain percent. Even so, it might charge the battery once a week. If all you do is use your laptop at the desk, you can remove the battery and it will last longer when you do use it.
IBM recommends storing a LI-Ion battery at about half charge.