Actually, it's a little bit more complex than that.
If the battery is NiCd, it's important to run it completely flat before you recharge it. Battery life is generally around 500 charge/discharge cycles before it refuses to play. NiCd are almost extinct now, but do check.
If it's NiMH it's not so fussy, and you can recharge as you wish. Battery life is still around 500 cycles.
Lithium Ion (LiIon) is different. Battery life isn't much dependent on number of cycles, but entirely on time elapsed since the battery was made. Some last longer than others, but if you buy three out of the same batch made on the same day, they will all start to lose capacity around the same time - regardless of whether they are used or not. Don't buy "old stock", and if you buy a new one, check the "manufactured date" on it.
Meanwhile - check the owner's manual very carefully indeed before you run your laptop with the battery "out". You could damage it. In some (not all) it's the battery that stabilises the power supply voltage to whatever the computer is designed to. If you run it without a battery in those circumstances, the voltage may be significantly over "nominal" and the machine may be damaged. The manufacturer would probably know what you'd done (from the nature of the damage inside) and refuse to honour the warranty.
Not all laptops are like that - but even so, I would never run one without the battery. A new battery is a lot cheaper than a new laptop.