Chewing gum
Import and sale are restricted, though personal possession in small amounts isn't the criminal offence its reputation suggests — you won't be searched for a stray pack in your bag.
Jaywalking
Crossing within 50 metres of a designated crossing is an offence with a real fine attached, and it is enforced.
Vaping
Banned outright, including for visitors — this is stricter than in many countries and worth knowing before you pack.
A few others
Littering fines increase for repeat offences, and eating or drinking on the MRT carries a small but real fine.