It is common belief that LSD: Dream Emulator does not end because you are allowed to play indefinitely.
This is true to some extent, but when the player completes a total of 365 dreams, a special cutscene will play and you will be restarted with the dream chart still filled out and the day counter going back to zero, symbolizing a new year.
The ending cutscene of LSD: Dream Emulator does signify something. The dream itself shows what is known as a Hatsuyume, a dream that occurs at the start of the new year supposedly signifying how lucky the dreamer will be in the oncoming year.
In the cutscene, Mt. Fuji, a hawk, and some eggplants are shown. In a Hatsuyume these signify Particularly good luck. More information on this topic can be found in the Wikipedia article linked above.
It's impossible to completely fill every space in the dream chart, as the filled spaces will eventually disappear after many dreams. Further analysis of the game files show that ENDING.STR, the previously known ending as shown below, is the only ending.
Since the only ending is called ENDING.STR, the developers might have planned to put another ending, or multiple, depending on what you have gotten on your chart.