I hope this helps.

Laundrywise-
1) Hangers (They don't provide you with it)
2) Washing Powder
3) A bunch of One-dollar coins to use coin operated washing machine.
Personal effects-
1) Toothpaste and toothbrush (Keep the ones they give you for display during standby cupboard)
2) Underwear (as many pairs as you need for the first two weeks when you will be CONFINED and you can safely stick with 6 per week)
3) Phonecard - The reception on Tekong makes using a handphone difficult. Having many spare batteries is only tedious and for goodness sake don't bring a charger because I know that in Tekong you may get charged if you charge you hp. Don't risk the temper of your section commander.
4) Munchies - Bring a stack. If you don't you might just realise how much you miss civilian food. The Cookhouse can be disapointing... but lunches can be excellent sometimes (You will get your best meal when you FIRST get there... the standard should expectedly get lower from that point. That first meal is actually for your parents benefit I believe- But SFI and NTUC are doing a great job so we shouldnt complain now should we?)
5) Gas Lighter - You will realise this has many uses after a week... especially in something called IFC (Individual Field Craft) Smokers, bring a spare. Don't bring a zippo. They can get stolen
6) Journal/scrapbook - This proved to be a great creative outlet especially in my early BMT days.
7) Reading material - Nice escapist, fantasy or even sci-fi stuff is great to relieve boredom and stress. FHM is most excellent. But try not to be caught reading it on the MRT back home on your first book-out. We don't want to reinforce the already hideous stereotype of the horny NSman. Stay away from 8 days or anything regarding entertainment because you are going to miss TV and I'll bet you'll almost never see the mess.
Medical
1) Panadol - general purpose pain relief
2) Anti-fungal cream - Whitespots are really common (feet, back) especially if the amount of training exceeds the amount of readily available uniforms. That's assuming you make an effort to change to a fresh set, but you might not have the time to do it (you'll find out why)
Beware footrot. IT CAN HAPPEN TO YOU.
3) Dettol - You can get it free from the medic, but only if you are openly bleeding and the fellow decides that it warrants the expenditure of his inconvienient to replace supplies. No offense medics. But BMT medics always seem to have an automatic assumption that all recruits are malingering.
4) Plasters - Again, you can get them free from the medic, but you'll like to have some on hand.
Lastly,
Bring a good attitude
Count your weekends.
There's only 9 of them so don't get yourself confined unecessarily.