LSD

LSD is by far one of the most unique games I have ever come across.
 
There isn't much of a goal in the game, nor does anything make sense but that doesn't mean it's a bad game. LSD is a free-roaming game dream simulator full of alien-like creatures, strange tunnels, and full of Japanese culture, which isn't surprising considering it's a Japanese made game. (That also counts for the overall strangeness of the game.)  Some players may find the game boring or dumb with the lack of a goal, but as your progress deeper into the game I feel that is when it becomes most interesting. 
 
You'll travel into new areas with the Linking system. Just by walking into a wall, object or person you'll be transported to a different area. This and the use of dark tunnels are the only way to really travel to new places. Everything you see will link you somewhere, just as long as you can walk into it. 
 
A dream ends when your either idle for too long, or fall off a cliff and wake up. You'll be taken to the main menu, and start a new game day. (or Dream)
 
You'll travel around the Graph and each dream is a new experience with trippy colors, different faces on the floor and walls, and more and more stranger and odder characters within the game. (Probably the oddest NPC I've encountered is The Grey Man, which reminds me of the G-Man from the Half-Life series.)
 
I think that if you ever come across a copy of LSD, your best bet would be traveling all the way to Japan, you should buy it in a heartbeat. It's a rare title, that shouldn't go unnoticed.