Widely regarded as one of Europe's most beautiful Gothic cathedrals, the York Minster is a reason to come to York in and of itself. The space defies description: a soaring nave, high pointed arches, towering stained glass windows, and a wealth of historic monuments and statuary. It is something one really needs to see for oneself.
The Five Sister's window opposite the main entrance is stunning. Also, be sure not to miss the chapter room, behind the altar area and to the right: the octagonal space was designed for increible acoustics, so that conferring officials in the stone seats around the perimeter could hear one another from opposite sides of the room.
Now, for the technicalities. The Minster actually encompasses three different attractions, with a somewhat complicated admission-pricing arrangement: details are available at http://www.yorkminster.org/index1.html. Discounts offered for children, students, and seniors. Of the three sites, the Minster proper (5GBP) is the main attraction, and includes a free guided tour. For most visitors, the Minster will probably suffice.
Those interested in architecture, Roman or Norman history, or in Church treasury items will also want to visit the Undecroft area (4GBP; 7GBP for Minster and Undercroft), which details the Roman and Norman origins of the site and includes a very informative (and free) audio tour.
Finally, fit visitors may want to scale the tower (3.50GBP), though be advised that the tower closes before the rest of the church. On your way out: don't miss the bronze statue outside the main entrance commemorating the proclamation of Constantine as Roman Emperor in 306 AD, which happened at the Roman fort whose site is currently occupied by the Minster.