Things to consider if:

You are removing the battery while on AC power:
Pros:
• Preserves charge cycles
• Keeps the laptop battery temperature lower thus slowing the aging process
Cons:
• Lose the notebook battery as backup power during power outages and voltage drops
• Unsaved work will be lost and data may be corrupted without backup power
• UPS (uninterruptible power supply) needed to serve as backup power source

You are leaving the battery connected while on AC power:
Pros:
• Battery serves as backup power during power outages and voltage drops
• More convenient for “grab-and-go” use
• Battery doesn’t require sufficient warming time (as it would after being stored in the refrigerator)
Cons:
• Loss of charge cycles
• Battery’s temperature is higher on AC power resulting in accelerated aging