Hi, I have been getting paid as self proprietor this year (2013). I have not formed any LLC or any other kind of company. Is it possible to form a company in 2014 before filing for tax return of 2013?

Yes, but you would still have to file as sole proprietorship for 2013.

What advantage do you think forming a business entity will give you? Most of the advantages are protecting your personal assets from a suit against the business.

Scott has it right.

If your income is expected to be at or below $150,000 for 2014, register the LLC as a "disregarded entity" which retains your sole proprietorship status, which is the easiest one to maintain for bookkeeping and taxes. The advantages of a S-corps do not really kick in until the income hits the $150K, and you can always change it later.