Can I pray with nail polish on?

No, not with regular nail polish. Normal polish forms a waterproof layer, so water can't reach your nails during wudu and your wudu isn't complete. Remove it before wudu. There's a handy workaround though: polish applied after wudu doesn't affect your prayers until that wudu breaks.

Why polish is a problem

Wudu means water has to reach the parts you wash, including your nails. The Quran describes it like this:

فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ "...wash your faces and your hands up to the elbows..." Quran 5:6

Once, the Prophet Muhammad ﷺ saw a man who had left a spot the size of a fingernail dry on his foot. He told him, "Go back and perform your wudu well" (Sahih Muslim 243). If a nail-sized dry spot matters, a full coat of polish does too.

The "polish after wudu" trick

Wudu stays valid until something breaks it, like using the bathroom, passing wind or falling into a deep sleep. So:

Make wudu.
Paint your nails.
Pray as many prayers as you like while that wudu lasts.
Once it breaks, remove the polish before your next wudu.

What about "breathable" or "halal" polish?

Some brands sell water-permeable polish and market it as halal. Opinions are split. Some scholars accept the brands' tests, while others say a coating is still a coating and water doesn't truly wash the nail. If you're unsure, the safer choice is to remove it, or to follow a scholar you trust.

What's fine

Henna only stains the nail and doesn't form a layer, so wudu is valid.
Polish during your period. You don't pray during those days, so many Muslim women save their manicures for then.
Gel and acrylic nails have the same problem as polish and are harder to remove, so they're tricky if you pray five times a day.

What if I already prayed with polish on?

Many new Muslims only learn this after weeks of praying with painted nails. Don't let it shake you. Scholars differ on whether prayers made in genuine ignorance need to be repeated. Many say they don't, and others recommend repeating recent ones if it's easy. Either way, Allah knows you were trying. From today on, simply remove the polish before wudu. See Do I have to pray while on my period?

Key points

Regular polish blocks water, so wudu isn't valid over it.
Polish put on after wudu is fine until that wudu breaks.
"Breathable" polish is debated among scholars.
Henna is fine anytime.

Tip: Keep a few nail polish remover wipes in your bag. They make it easy to get ready for prayer at work, school or when you're out.