I would say the Cathedral in Cologne (the Kölner Dom, as the natives would say) is a must see, but it's really more of a can't avoid. It is the largest Gothic church in Europe and boasts the second largest church spires and the largest church facade in the world.
And it's located about 50 feet from the exit to the main train station...
Like I said, you can't miss it!
I went to Cologne (Köln to the natives) last weekend with the teacher I'm currently living with. We only had the afternoon in the city, and the bulk of the time was spent at the cathedral. After a careful inspection of the inside, we decided get a new perspective on things.
1.50€ later we were on our way up the 533 step spiral staircase that leads right to the top of one of the spires.
Of course I tried counting steps, but once I got to 33 and said to myself "only 500 more to go!" it got a little depressing and I gave up. The majority of the route is a single spiral staircase, maybe about 2 feet wide. Oh, and did I mention everybody is going up and down the same staircase at the same time?
For someone who's not claustrophobic at all really, being trapped in this never-ending, never-beginning, dizzying whirlwind of steps with no less than 75 others was making even me a little anxious.
However, between the getting to see the giant church bells (seriously. Respect, Hunchback.) and the view from the top over the whole city and the lovely Rhine River, it was totally worth it. Just see for yourselves...