Toluene or xylene are very similar non-polar solvents, but don't have the same level of carcinogenicity as benzene. You still don't want to be inhaling them regularly or in large quantities.

The sad chemical being phased out is tetrachloroethylene (a.k.a. brake cleaner), which is nicer than its replacement (acetone), because it's non-flammable. It's also a better solvent for oil/grease than acetone.