I would never us graphite in a lock tumbler, it just plugs them up. I worked as a locksmith for 8 years, and we used Tri-Flow Teflon spray. WD-40 will work well for flushing the cylinder, but it evaporates and leaves nothing behind to lubricate for normal use.
You can try to clear out some of the gunk by spraying quite a bit of teflon in and working the key in and out with out turning the cylinder. Keep spraying in more oil to flush out the gunk, you will need lots of rags to catch the blackend oil. You can keep repeating that process till the oil comes out clearer. If your key doesn't have cuts that are alternating high and low, it won't work the pins or wafers as well while cleaning. You can use any of the same type of key that might have better cuts to do this.
Also if your key is almost wore in half (GM) .. get a new one! It will save you some headaches. The sticking may not be the gunk at all .. it could be a copy that is not cut accurate. Always make copies from the original key, not a copy of a copy.
If flushing doesn't work, it will need to be removed and cleaned like ttoyoda described. Always regularly oil lock cylinders, especially the doors in road salt conditions.
