My goals are knowledge, integration, and bonding.
Initially, I tried my first psychedelic because a friend convinced me that he had discovered the answer to life, the universe and everything by taking LSD. He begged me to try and and to put off calling him crazy until I had actually experienced it myself. I agreed, and decided that I had also found the answer to life, the universe and everything.
After that, I continued tripping occasionally until I felt I had learned everything I could from it. At that point I stopped. I'm able to understand the experience while sober and have completely integrated the experience into my sober understanding of reality.
Same goes for magic mushrooms. I tried them and then continued using them until I no longer could gain anything from an experience. Then I stopped.
I haven't tried DMT yet, but my intent is the same. I hope to experience hyperspace for myself, and learn until I feel that nothing more can be gained in terms of what I can carry back with me to sober life.
Another goal is to use psychedelics as a bonding experience with friends who are willing to try them, or with those who have already used them.
Some people I know use LSD once a year to re-examine the year with a fully-expanded consciousness. This seems respectable to me.
For me, though, the magic and escape is just a side bonus during the trips. The awe, knowledge and bonding stay with you forever.