I'm a little late to this party. Here's my advice, some of which might already have been mentioned:
Credit Cards * Never spend more on your credit card than you can pay off at the end of the month unless really necessary (emergency medical bills, house burnt down etc). The interest on credit cards is painful.
NEVER miss a credit card payment even if you can only afford the minimum sum due. Missing payments can wreck your credit score and make it more expensive to get a mortgage down the road.
No one needs a wallet full of credit cards, especially the 'lifestyle' ones which will encourage you to spend more. The only one you really need is a general purpose one with cashback. You might also want one with good cash-to-flier-miles conversion if you intend to travel, but in general a fresh grad's pay won't allow you to generate many miles that way.
Make a sticky note with the dates you received each of your credit cards. Call the card issuer every year to get them to waive the annual fee.
Insurance There are many kinds of health insurance. Offerings in the same category from different providers can vary drastically. An independent financial advisor can help you pick plans across the providers, just don't let them sell you anything investment-linked. Some general tips:
Do not buy investment-linked insurance. The management fees destroy your yields and most do not guarantee returns. Insurance agents push these like mad because they get ridiculously high commissions from them. Do not let agents use the argument that you should be forced to save. Develop the willpower to save and invest.
Round off your basic insurance portfolio by age 30 as premiums increase significantly after.
Don't let insurance agents scare you into buying unnecessary plans. My gf was talked into spending $1000+/month on insurance when she only grosses $4,000+/month. Many of her plans weren't even competitive with those of other insurance companies.
Your first priority should be hospitalisation/surgery insurance. Medishield is cheap, cheerful, covers most of the basics, and can be paid for out of your CPF. Sign up for this ASAP. Later on, you might want to consider a more comprehensive plan that can also be paid for using CPF. Details on plans like these: http://mycpf.cpf.gov.sg/CPF/my-cpf/Healthcare/General_Info_MSH-Scheme.htm
Critical illness insurance is good to have but can cost. KIV this for when you earn a bit more.
Life/total permanent disability and disability/income-replacement insurance are not of high priority to someone without dependents. Get before you turn 30, no rush. Investigate term insurance vs whole life insurance. The former is cheaper up till age 65 but the latter could be cheaper if you live to a ripe old age. I use a mixture of plans myself and intend to let the term plans lapse when I hit 65.
Investments and Trading * If it sounds too good to be true, it probably is.
Don't bother with MLMs unless you're getting in near the top of the pyramid.
The earlier you start investing the greater compound interest works in your favour. Start now. No amount is too small to start with.
Most people can get away with just contributing regularly to a portfolio of blue-chip dividend stocks (bank preferred shares, telco preferred shares etc... find a list of such stocks here: http://www.topyields.nl/Top-dividend-yields-of-STI.php) and ETFs/index funds.
Learn the vocabulary. Like, what is the difference between an ETF, an index fund, a mutual fund/unit trust. www.investopedia.com is your friend.
Avoid mutual funds/unit trusts and other managed funds like the plague. See: http://www.nytimes.com/2015/03/15/your-money/how-many-mutual-funds-routinely-rout-the-market-zero.html?_r=0
If you invest in a LLP, LP, or Pte Ltd company, you stand a good chance of not getting anything back if said company folds even if the directors of the company remain personally wealthy.
Taking on debt to pursue an investment is not wise.
Very few day-traders can make a living doing it. Ditto for FOREX traders. Don't let anyone convince you otherwise, especially if they're trying to get you to pay them to learn how.
Consumption * Don't try to keep up with the Joneses. Every dollar spent on a frivolous purchase is one less dollar generating returns for you. Indulge once in a while but the 70-30 rule mentioned by /u/hannorx is a good guideline to follow. I found the advice at http://www.forbes.com/sites/robertberger/2015/03/03/how-much-of-your-income-should-you-save/ to be a sound extension of this.
Branded watches and jewelry should never be referred to as 'investments'.
Buy whatever you can second-hand. I personally love expat relocation garage sales.
Don't be afraid to say no when colleagues invite you out after work. Such a night out would typically cost you $30-60.
Same for weddings. Only attend the ones of your closest friends. Here's a red packet market rate guide: http://www.weddingangbao.com/
Make sure you have two well-fitted suits, two comfortable and smart pairs of shoes, and six shirts that make you look awesome. Replace them when they're worn out. Anything beyond that should be regarded as a luxury. Getting these done at reputable tailors when on holiday in SEA /China can save you a lot of money.
Only buy a car if you really need one. Don't forget that beyond the instalments and petrol you also have to pay for car insurance, road tax, servicing, and other repairs. Brake pads, tyres, spark plugs, engine seals, the serpentine belt, batteries all wear out and have to be replaced. A total engine overhaul to replace seals would likely be needed before a car turns 10 years old and will set you back thousands.
Also note that the outstanding loan on the car will count against the maximum amount you can loan for a mortgage.
Starbucks and its ilk are the downfall of many a budget.
Generic Tips * Find out how to claim NS make-up pay ASAP.
Don't forget to file your income tax. Educate yourself on the deductions you might be eligible for.
Don't lend money unless you're okay with not getting it back. Signed IOUs and photos of ICs are of no use when chasing a debt.
Keep interviewing with other companies even if you have no current plans to leave your job.