Steam cleaner!
I bought a Wagner steam cleaner and I have gotten stuff clean that NEVER would have came clean before. It is gentle since there are no chemicals, just blasts of steam. I love it! Places that I ordinarily would have just painted over to freshen them up thanks to the kids, I just shot with steam and voila, the gunk rolled right off, I wiped it with a cloth and it was gone.
The steam cleaner works great on carpets too. I had some stubborn spots that my carpet shampooer wouldn't remove, the steamer took them right out.