Several good products have been listed in the other replies, and most will do the job of cleaning carbon and copper.
The petroleum/ammonia based cleaners like Hoppe's, Shooters Choice, Butche's, G96, work well, for a quicker cleaning CR-10 and Sweet's 7.62 will fill that need.
For the new generation of cleaners which are water based, Wipe Out (foam or liquid) Aqua Clean, Bore Tech Eliminator or 1st Choice Bore Cleaner, they will perform carbon and copper removal equally as well. They have much less of an odor to them, which makes cleaning indoors less of an issue for the rest of the family.
When leaving solvents in the bore, remember they are a liquid even the foaming products return to a liquid fairly quickly, this means that the product has a tendency to migrate to the lowest point. This will effect the degree of bore solvent concentration throughout the bore, and could have the effect of more or less cleaning in parts of the barrel (top vs. bottom).
I have seen several incidences of allowing the foaming cleaners to expand into the receiver, getting into the trigger and the bolt stops on Remingtons. This did not have good results for there function.