If the winds arent very strong and things aren't too busy, ATC will usually have no problem allowing you to take off in the direction the wind isn't favoring. Its only reccomended that you take off into the wind, not required. Also, I know there are some runways in the mountains or have other obstructions where you can only take off one direction and land the other.
I've actually had the experience when I was living in Japan and fying out of an aeroclub on an airforce base. They badly needed to resurface the runway, but they didn't want to shut it down for a few months, so what they did is they decided to do it half at a time. So for a while, you could only take off in one direction and land in the other. Whenever we wanted to stay in the traffic pattern and practice landings it made things real fun. We'd take off runway 36, and do a left 90 degree turn. Fly that way for a minute or so, then make a right 270 degree turn and land on runway 18. Run to the end of the runway, turn around, and take off again.