Experienced twice liao.
Once, on a TRANSCAB (as expected). Board at Kranji MRT Stn exit,
going to Yishun Central. Cabby used this route:
Kranji MRT/ Woodlands Rd > Turf Club Ave > SLE >
Mandai Rd > Woodlands Rd > opp Kranji MRT >
Woodlands Ave 3 > Woodlands ave ?? > Gambas Ave >
Sembawang Rd > Yishun Ave 5 > Yishun Ave 2.
Then i asked this malay cabby where is he going.. he got the cheek
to reply:"Thats why.. i also dont know"
By the time reached opp Kranji, meter already $6+. Lucky not i
paying 
2nd instance was this Chinese NEw Year 2nd day. Called advance
booking for cab from Seletar Rd to Changi Airport.
Shortest Route: Seletar Rd > Jalan Kayu > TPE > PIE >
ECP > CGA
This comfort cabby got another idea: Seletar Rd > Yio Chu Kang
Rd > Hougang Ave 2 > Hougang Ave 3 > Tampines Rd > TPE
> PIE > ECP > CGA.
In the end when he was about to turn right, i asked him why he
didnt go straight towards jln kayu.. he said: "Oh, want to go there
ah?" then he proceeded.
think i mentioned tis b4.