The basic 1040 Form is the one used by United States citizens or residents to file their annual income tax returns with the Internal Revenue Service (IRS). However, there are many different types of 1040 forms available; in fact the term 1040 describes a whole series of different IRS forms meant for people with different circumstances and situations. There are six different types of 1040 forms regularly and there was one special one that was only applicable in the 2007/2008 tax year (the 1040EZ-T, used to deal with refunding telephone excise taxes to people otherwise excused from having to file an annual return).
The standard Form 1040, also known as the long form, is the one that allows the most options and deductions and is generally used by people trying to minimize their tax bill or maximize their returns. Allowing eleven different supplementary schedules, this is by far the most complex of the 1040 series and is usually only used by professional investors or people with extremely complicated tax situations.
The 1040A and the 1040EZ are easier, simpler versions of the 1040 form, used by people with less to report or declare than people using the standard 1040. These easier to use 1040 forms are restricted to people that make less than $100,000 per year and those that opt to take standardized deductions as opposed to itemized ones. The overwhelming majority of Americans use one or the other of these less complex forms for filing their annual income tax returns.
The 1040NR and the 1040NR-EZ are the income tax return 1040 forms used by nonresident aliens in the United States that are required to file. The 1040NR is the more complex of the two, allowing for many more options while the 1040NR-EZ is very much akin to the 1040EZ and has many of the same restrictions on who can file using them. These are basically the forms used for nonresident aliens that have lived in the United States for less than five years.
The last of the 1040 forms series is the 1040X, which is used to make changes or amendments to standard 1040, 1040A, or 1040EZ forms that have already been filed previously. Often used in conjunction with IRS Form 3115, the most common reason for filing a 1040X is to get a refund on taxes paid previously, though sometimes they are also filed in order to fix mistakes made previously before they are discovered by the IRS.