I have a Logitech webcam C615 that I'm trying to hook up with my Mac mini (2011). This may sound silly, but is there a way I can install the software without having an external CD drive? I had no idea that it came with a CD for installation or I would have made the 30 mile trip to the Apple store. :(
If you have access to any other computers that do have a CD drive, you can use Drive Sharing
As Apple says,
This convenient feature of OS X lets you wirelessly “borrow” the optical drive of a nearby Mac or PC. So you can install applications from a DVD or CD and have full access to an optical drive without having to carry one around.
Even with a CD drive available, I would recommend first checking the manufacturer's website for the latest drivers because there's a good chance they've been updated since the included CD was made. I would only bother with the CD if it contains bundled software or drivers that are unavailable online.
It looks like you should be able to download the latest drivers for your webcam from Logitech's downloads page for the HD Webcam C615.
If that download doesn't contain everything you need from the CD, then I would recommend following Daniel's answer.