I'll start with the standard issue 03 x Tekong Ghost Stories
As far as I know, there is never training on Thursday nights. This is one of those things that you won't realize until someone tells you about it, and then you go "oh".
The story goes, there was one Route March where one of the recruits disappeared. Everyone thought he was with someone else - people in the march thought he was with the medic, since he was feeling unwell; medic thought he was garang and pressed on; etc.
A search party was sent out, but could not find him anywhere. It was not till the next day that his body was found. There have since been reports of sightings of him.
For the creepier, more fleshed out story, follow this link.
An often heard variation states that his innards (intestines, stomach, etc.) were discovered laid neatly in front of his body, in exactly the same way as a Field Pack inspection.
Grandma and her Little Girl
Ah, this is just plain famous.
If you sleep in Bed 01 of your bunk, keep to lights out timing. The story goes, there is this couple - an elderly woman and ostensibly her granddaughter, who go around counting the sleeping people. From what people tell me, the worst thing you can do is to peep, because exactly when you peep, the little girl will be standing right in front of you, staring straight into your face and alerting her grandma that you are awake.
A variation states that it is instead a boy, with a basketball. He comes to ask for a companion, and his grandma will tell him not to wake you up, to which he replies "korkor (brother) where got sleeping?"
I have heard of people who mistake their sergeants for this ghost, screaming when they come in for a spotcheck.
Jacob's Ladder
Now, as I have never done SOC, I am familiar with neither the grounds nor what goes on around there. What I have heard, however, is that there are white figures who sometimes stand around this obstacle, or even sit on the top of it.
This story has surprisingly avoided being exaggerated over time, so it sounds pretty credible. In addition, I have heard people talk about it without realizing that so many others too have witnessed it.
Others
Trees
This is a more everyday encounter, as you do your business. Your commanders will teach you how to ask for permission from the occupant of the tree. I remember a Russell Lee story about possession after someone used a tree without asking. A particularly memorable part was that the ghost complained about there being insufficient trees for all of them.
Toilet (Personal Story)
Water parades can really spoil your night by waking you up to pee, and worse yet, these experiences can expose you to some eerie happenings.
One night, at 3am, I entered the toilet to pee. There was nobody inside the toilet - I know this because the automatic toilet lights are off, and these are usually very sensitive so it cannot be that someone sneaked in and avoided it. Halfway through my peeing, though, one of the showers suddenly turned on. Instantly my goosebumps rose.
I hurriedly finished my business and as I turned to leave, a toilet bowl (these are right behind you, 2 metres away from the urinals) flushed.
Needless to say, I sprinted all the way and jumped into my bed, eager to quickly fall back asleep.
Pork
Tekong was an old Malay village and cemetery, so please please please don't do anything stupid like bringing this to bunk with you.