Which is the coldest planet?
Short answer: Neptune is the coldest planet on average, but Uranus has the coldest temperature ever recorded on a planet in our Solar System.
Long answer: In our Solar System, the planet with the lowest average surface temperature is Neptune at around -214°C. Being a gas giant planet, it doesn't really have a surface as such, so we can think of its icy water layer as the closest thing it has to a surface. Planetary scientists take temperature readings from where the atmospheric pressure is 1 bar (100 kPa), the same atmospheric pressure as sea level on Earth.
Uranus, even though it is closer to the Sun, holds the record for the lowest temperature ever recorded on a planet. It's not much different to Neptune's average: -224°C. However, the average temperature of Uranus is around -200°C, making it warmer than Neptune overall.
Both Uranus and Neptune are such a long way from the Sun that they don't get a lot of heat from it. Most of their heat actually comes from their own interiors, and is trapped fairly efficiently by the methane in their atmospheres.
Note: Before 2006, the answer to this question would have been Pluto. However, it no longer counts as Pluto isn't officially a planet any more.