I got a job in the summer of 1965, programming a PDP-6 to put a model of a protein molecule on the display, as a stick figure. The molecule was 3D and the display was of course 2D, so I had to simulate depth. I used perspective, shading, and motion.
The idea of the display was to allow a human crystallographer to evaluate the actions of another computer program, to see if they seemed real. The other program, running on an IBM 7094, was bending and twisting the molecule so as to optimize something like bonding energy.
This was hard, and I only had a couple of computer courses and a little random hacking under my belt at the time. The hardest part was programming the modem that was networked to the IBM 7094. It took me all summer just to get something going.
Edit: There are a number of applications that used the CRT on either the PDP-1 or the PDP-6. These were all much more impressive than my efforts. A partial list follows:
SHRDLU. This is a program that could manipulate a virtual set of blocks using a virtual robotic arm. It acted on the blocks, based on natural language input from the user. The CRT was just to let the user see what SHRDLU was doing with the blocks. The main focus of SHRDLU wasn't the display. It was early exploration of natural language recognition.
Expensive Desk Calculator. This was a predecessor of VisiCalc, Lotus 1-2-3, Excel, or any of the electronic spreadsheets.
Expensive Typewriter. This was a predecessor of Word*Star, Word Perfect, Word, or any of the word processors.
Spacewar. My favorite, and already mentioned in another answer. Often used as a demo of the capabilities of the CRT. Predecessor of Space Invaders, Asteroids, or any of the video games.
Project PEPR. (Precision Encoding and Pattern Recognition) This was about automating the scanning and evaluation of millions of bubble chamber photographs. The CRT was used for, among other things, showing the user an image of the current photograph.
I don't know whether the Harmony Compiler belongs in this list or not. I'm not sure it used the CRT. But it sure used the speakers! This was a predecessor to the audio CD, MP3, and all that.