Koopa Troopa Plains

Koopa Plains is an anomalous course found somewhere in Super Mario 64 (Reports vary on the location of the area). The course is most commonly described as a hilly grassland area looking a lot like the cartridge art of the game. Some other features of the level include small park areas, Koopas, ponds, & (rarely) a few forested areas. Almost every report says something different about accessing the level.

Missions
Missions vary from report to report, but here are a few of the common ones.

Red Coins in the Green Garden / Reds Around the Park / Red Coins in the Pond
There have been many reports of red coin missions with many different names.

Drain the Fountain / Underneath the Fountain / Secret in the Park
Most reports also include a star relating to a water fountain in a park area. Some reports even state that Mario must go underneath the fountain to obtain a star

Delicious Cake
One of the less common stars has Mario enter the Delicious Cake level to get a star.

Bowser's Invasion
In this star, Bowser would show up in the level (usually with some troops) and chase Mario around the level leading to the theory that this is where the cartridge art takes place.

Report No. 1
One of my friends talked about this in passing conversation once.

"So, one day I when was playing SM64 I think that I found a secret 16th level. When I first turned on the game, I noticed something was off (little things like music and colors). Entering the castle, I went into Big Boo's Haunt (I still had to complete that one) and instead of entering it like normal, I came out in a completely different level (it was called like Bowser Park or something). The next thing I remember is selecting star one (it was something related to the fountain) and wandering around. The place looked sorta like the park we have in our town." I asked him if he did anything the day before but he said that he didn't. After that, the conversation transitioned into a talk about town parks.