When I was in college, Cover Girl came out with a nail polish that you could apply to your nails, let dry, then peel off when you were tired of it. The formula was never perfected, I guess, because it was discontinued after a few months. I'd tried a couple of colors out before they all went on clearance - one worked great, and the other one peeled off on its own accord. Very frustrating.
Sula Beauty has now reinvented this wheel by releasing a line of nail polished called Paint & Peel that doesn't require polish remover. As the product's name implies, simply paint your nails, then peel off once you're ready to start over with a new color or go bare. Based on the FAQs found on the site, it sounds like you can expect each coat to last at least full day. To keep it going beyond that, apply Sula's Clear or Metallic top coat for extra durability.
The polish is "free from gormaldehyde, toluene and phthalates and is also free of the remaining cancer-linked ingredients still found in standard polish." Sounds like you can't lose with this polish!
Paint & Peel comes in two collections: the Sula Collection, which includes four colors that are more traditional for the nails, and the Trend Collection, which offers users a few more "out there" colors including Dove/grey and Crush/dark purple. Currently you can buy them through Sula's website or at a few locations through the US and Canada. Each bottle is $9-$10 - I just might have to try these!