A star or constellation that is always visible (i.e. that never sets) is known as circumpolar. Dependent on where you are in the world different stars will be circumpolar. To explain this more fully we need to understand why the stars set at all.

The stars above our heads are to any casual observer, fixed in their positions above us. In reality they move but the motion is so small and subtle from our distant perspective that they can be considered motionless for the sake of this example. As the Earth rotates they seem to move across the sky and as we moved around the sun they rise and set a different times just as the Sun does, with the seasons.

If you imagine the Earth’s surface extended outward as a sphere. First you have the molten mantle and then the Earth’s crust on which we live. Then you have the lower atmosphere which we breathe and in which mountains and oceans exist. Go even higher and we have a larger sphere on which planes fly about. Higher still there is an imaginary sphere which Satellites move around on and then a larger one still going outward farther and farther until we have what the Greek’s coined the Celestial Sphere. Although they believed it more literally, the idea of a giant Celestial Sphere on which the stars sit is very useful, it acts like a globe for the constellations and it is shown in the graphic above.

So extended outward from the Earth’s north and south pole are lines which reach out to the Celestial north and south pole. The Celestial equivalents of longitude and latitude are Right Ascension and Declination. The celestial equator lies in line with the Earth’s own equator (by definition).

Because the Earth is tilted on its axis, the Sun traces a path around this sphere known as the Ecliptic. If the Earth were not tilted then the Ecliptic would lie exactly on the Celestial equator. But in reality the two are slightly at an angle.

The Sun, the Moon and the planets all move around our sky along the Ecliptic and therefore the twelve constellations which lie on the Ecliptic are always home to the planets. These are the constellations of the Zodiac.

Now all of this explanation is to put in context the fact that if you sit at the North Pole and look directly upward, you will see the star Polaris (or the North Star, in the constelation Ursa Minor), which conveniently lies almost directly over the North Celestial Pole. It will not move at all because of your location on the Earth. At the Horizon you will see the signs of the Zodiac rising slightly over the horizon and then dip slightly under it, following the Ecliptic over the course of the year. In between you have various other constellations which never leave the sky. In fact almost all of the stars in the Celestial Northern Hemisphere will remain visible to you on any night of the year.

A similar situation would present itself if you sat at the South Pole, only this would involved the constellation Crux, rather than Polaris, and all the Southern stars would remain with you. However if you sat on the Equator or in the Tropics, you would not see a sky that rotated but kept the same stars, instead you see a vast rolling sky with one constellation of the Zodiac high above your head at all times and Polaris and Crux sitting at opposite ends of the horizon.

So the question of whether there are any constellations which are always visible is only answered by knowing your location. So, at the poles, all constellations that you can see are circumpolar; at the equator none of them are. In between the answer is that some of them are.

From Cardiff and other similar latitudes the following are circumpolar constellations:

Ursa Major
Ursa Minor
Draco
Cephus
Cassiopeia
Camelopardalis
Lynx

This answer also explains why you need a different planisphere for different locations.