Method 1:
Fingernail paint peeling does not work unless there are paint droplets formed on floor. This method does not work on smudges.
Method 2: Goof Off. Absolutely NOT. It takes EVERYTHING off of your floor. Not only does it remove the paint but it also removes a layer of varnish! It's very toxic and should only be used in a well ventilated room. Windows open please! Actually don't use this product at all!! It's stinky and makes the surface that it was on sticky.
Method 3:
The final product and greatest is Orange Squeeze citrus oil that I purchased from Lowes. I didn't think this would work but this was the second time that a rep from either HD HQ (Home Depot Headquarters - my secret obsession) or Lowes had recommended a citrus oil. I purchased a small aluminum pump bottle and tried it out! Love it. Here are photo's.
This is the bottle next to a blue latex paint stain that had been on the floor most likely for over a year or two.
Here is a close up of the blue paint.
This is less than 10 seconds after I sprayed.
So this Orange Oil gets 5 stars! It smells great, it's non-toxic and takes no time at all.
FYI: This oil seems to work on coated (for lack of a better word), non-porous surfaces (varnished wood, laminate and vinyl). I have not tried this on any other surface. This is an oil-based product so wearing old, "work" clothing is recommended.