Are there any kind of troubles that I could get into if I use the same install CD on two laptops? I've just received a laptop from my workplace, but apparently they lost the install CD, and I want to use my own to "clean up" the laptop.
In writing this answer, I'm assuming that you're speaking the truth when you say your workplace lost the install CD for the laptop--that is, you have the legal right to install it, but not the physical medium with which to do it. I'm not in any way encouraging you to pirate software.
That said, when you install Snow Leopard, it won't ask you for a serial number. If the installation disc came with a computer, it will likely only install on computers that are the same model as the one the disc came with--so, for example, the installation disc that came with an iMac won't work on a MacBook Pro. The retail version of the OS, however, will install on the laptop, run normally, and download and install updates without a problem. It will do all of this even if you've used the same disc to install the OS on another computer, because there is no protection scheme in the OS to prevent this.
Edit: As Samantha Catania says in another answer, the discs that come with a computer are machine-specific, in the sense that they will only install on a very specific model of computer. If your work laptop is a different model than the model the disc came with, it just won't install at all. It'll stop before it does any damage, though, so (again, repeating what Samantha already said) it wouldn't hurt to try. Most likely, though, you'll need either an installation disc for the exact same model you're trying to install on, or a retail disc.
The gray installation disks are model specific (i.e. they only contain drivers for the specific hardware which they came with e.g. an iMac or a MacBook Pro). There is no DRM on the disks, nor other copy protection. You can install on multiple computers but all must be the same model.
If you have a black retail disk you can only install OS X on multiple computers, and on any model (although possibly not models which were released after the purchase of the retail disk).