Under what circumstances would you file the long form 1040 tax return?

You're required to file the long form if:

• You want to itemize deductions
• You have self-employment income
• You make more than $100,000 per year
• You are required to file Schedule D to report capital gains

If none of those apply, you can file the short form (1040A), though anyone can choose to file the long form 1040 instead if they want. (The long form has the most options, and allows more credits, but anyone eligible for those credits is likely to be required to file the long form anyway; the only real "decision" involved for most people is deciding whether to itemize deductions or take the standard deduction.... if you're using the standard deduction and are allowed to file the 1040A, there's probably no advantage to you in filing the 1040 instead.)

People with no dependents (other than themselves and a spouse) and meet a few other criteria can file form 1040EZ instead of 1040A. Again, there's no real "advantage" either way, other than that the 1040EZ is slightly simpler.