Of course. That's exactly why I became immune to the common cold virus when I was one year old. I've led a blissful, cold-free life since then thanks to my conferred immunity at that tender young age.
Disclaimer: I'm not a virologist, but I DID stay at home last night.
There are literally thousands of varieties of the common cold virus. You are probably immune to each one you have had in recent years, but that leaves a lot of infection still out there.
There are several strains of ebola, it would be interesting to know if having one strain confers immunity to the others as well. If so that would leave hope for an attenuated vaccine (like the smallpox vaccine) for ebola....
There are hundreds of different viruses that cause the common cold. If you never develop symptomatic common cold illness, I would say that there is something about your immune system that prevents you from having symptoms.
I rarely get colds. I think I might have had one a couple years ago. Then again, it might have been allergies.