I use my MacBook Air as a desktop. Should I leave the charger connected all the time or should I deplete the battery and then recharge? Which is best for the battery?

Keep the computer plugged in whenever possible.

If you keep the computer always plugged in, make sure that at least twice a month

run it on battery until battery charge level drops to about 50-40%.

Please don’t discharge the battery completely. Discharging battery completely will reduce battery health.

For more useful info:

Section: Optimizing Battery Life

http://support.apple.com/en-us/HT204054

Quoting from below linked article.

“The question is often asked: “Should I disconnect my laptop from the power grid when not in use? Under normal circumstances this should not be necessary because once the lithium-ion battery is full, a correctly functioning charger will discontinue the charge and topping charge will only engage when the battery voltage drops to a low level. Most users do not remove the AC power, and this practice is safe.”

http://batteryuniversity.com/learn/article/bu_808c_what_the_user_can_do

Follow two rules for best battery performance.

If you connect to the charger all the time, at least once per month use it under battery power to about the 40% charge level before reconnecting to the charger.

Do not discharge the battery completely. That will shorten its useful life. When you see the low battery warning, terminate the session and reconnect to the charger.

Here is some Apple battery information:

http://www.apple.com/batteries/

Ciao.