For sure you must not use nail polish remover or try to scrape it off with a razor blade. You may be able to safely remove nail polish from wood furniture by spraying it with hairspray, however. You must test it on a hidden place first. Some finishes cannot even withstand hairspray.

Follow these steps from How to Clean Stuff.net:

1. Spray the nail polish with a good amount of hairspray. Wait 15 seconds for the nail polish to dissolve.
2. Wipe the spot with a towel that has been dampened with warm water.
3. Mix a good amount of dishwashing detergent with hot water to create a very sudsy cleaning solution.
4. Dip the sponge ONLY in the suds (not in the water). Place it on the affected area and allow it to sit for 15-20 seconds.
5. Clean the area with the sponge. Do not use an abrasive scrubber on the surface, use only a soft sponge.
6. Wipe the area clean with a towel.
7. Repeat steps 4 through 6 until the hairspray and nail polish are completely gone.
8. Dry thoroughly with a towel.
9. Add a wood polish or oil to protect the surface.