Now laptop batteries are very expensive, however I have a slightly beefy Dell Inspiron 1525 laptop with a half year old battery that works fine.
Other than complete depletion, of which I have heard ruins the life of a battery such as this, the charging will be done by the laptop itself plugged in to at least prevent over/improper charging.
Could I use this type of battery (after regulating to 9/12v if necessary) to draw maximum 100-300mA to allow for a fairly extended battery life of one of my circuits?
I'd hate to waste it, being over a hundred dollars if I recall. Information is scarce on the web and people often just rip out the battery array inside and use them, which I assume is very hard if not impossible to maintain/recharge without the original charger.
I could of course buy some rechargables and put them in to an array, however those are costly (4-12 to have enough voltage in series) and I do not even think (possibly in the future I will obtain) a "9V PP3 L-ion" battery exists, which could be helpful.
Best Answer
The problem, as you say, is complete depletion.
It doesn't just ruin the life of the battery. It ruins the battery.
If a Li-ion or Li-poly battery gets completely depleted it is dead. Full stop. Replace it.
If you were to use Li-ion or Li-poly batteries then you will require some kind of battery management system to shut off the power before the battery gets completely depleted.
There are dedicated ICs around to do this exact job. For example - take a look at Texas Instruments' range of Battery Monitor chips