This question has been asked a couple of times, but it has not been really answered before.
So how long do you need to take to become a psychologist (in Singapore and other countries)?

I’ll start the topic with the explaining what the difference is between “membership” and “registration”.
Membership is where you become a member (of whatever level) of the psychological associations/societies. Being a member does not mean that you can call yourself a psychologist.
You have to be registered with the psychological boards before you can call yourself a psychologist. Psychological Boards are usually regulated by law. In the different countries, they use different words to indicate this: Australia – Registered Psychologist; UK – Chartered Psychologist; America – Licensed Psychologist. For the benefit of not confusing the readers, I will just use the term “Psychologist” here with the implication that we are talking about psychologists who are registered/chartered/licensed.

So how long does it take?

Australia:

At least 6 years. According to APS, “this can be achieved via a number of pathways, each of which requires as the first step a 3 year undergraduate degree in psychology plus an accredited 4th (honours) year, both of which must be accredited by the Australian Psychology Accreditation Council (APAC) and approved by the Psychology Board of Australia (PsyBA). These qualifications can be followed by:an accredited and approved postgraduate professional masters or doctoral degree, or an accredited and approved Graduate Diploma in professional psychology plus one year of PsyBA-approved supervised experience, or a two year PsyBA-approved internship. “

See this General Registration Standard as provided by the PsyBA. Also see SGPsychStuff’s post on the Australian system of psychological training and registration for a clearer understanding.

UK:

At least 7 years. You need a undergraduate honours degree in psychology, followed by a postgraduate degree or a research doctorate in psychology. This will be followed by at least 2-3 years of supervised training, based on the different areas of psychology. According to BPS:
“The total period of training, including time spent on the MSc and supervised practice must be a minimum of three-years full time or the part time equivalent. This applies to both full-time and part-time MSc courses.
A Society accredited MSc in Occupational Psychology grants exemption from the Stage 1 and the Stage 2 Structured Research Report. All candidates will be required to complete a minimum of two years full-time (or the part-time equivalent) of supervised practice under an ‘Approved Supervisor’.”

Please view the BPS page for the eligibility, benefits and process to be a chartered psychologist.
America: 

At least 7 years (Wikipedia said 4-7 years for the DPsych degree, which is the minimum education need.) You will need a postgraduate degree, which is a DPsych or Phd. Another requirement is 1,500 to 6,000 hours of supervised work, which can completed prior or subsequent to the postgraduate degree. Lastly you will need to pass the Examination for Professional Practice in Psychology (EPPP), as conducted by the ASPPB. There may be other examinations required other than the EPPP. The APA and ASPPB has articles for this process. This complications are due to the many states and legislation in America, hence there may be differences in different states.

What about Singapore?
It takes at least 5-6 years. It would be like the Australian system, where you need at least a Masters degree (the other two options are not available) with 1000 hours of supervised work. However the supervision in Australia are normally included in the Masters program, which may not be the case for the programs in Singapore.

See SGPsychStuff’s post on the pathway for Singapore psychology education for a clearer understanding.

Without registration, you should not be calling yourself a registered/chartered/licensed psychologist; otherwise it would be considered as unethical.