Which form is required to apply for an Individual Taxpayer Identification Number (ITIN)?

The correct form required to apply for an Individual Taxpayer Identification Number (ITIN) is the W-7. This form is specifically designed for individuals who are not eligible for a Social Security number but need a tax identification number to fulfill certain tax obligations, such as filing a tax return. The W-7 collects necessary information, including the individual's personal details and the reason for needing the ITIN.

The other options do not serve this purpose. The W-4 is used by employees to inform their employer about the amount of taxes to withhold from their paychecks. The 1040-NR is a tax return for non-resident aliens, which is not the same as an application for an ITIN. Form 8888 is utilized for allocating a tax refund to multiple accounts, and therefore does not pertain to applying for an ITIN. Understanding this differentiation is crucial for ensuring compliance with tax responsibilities for individuals who require an ITIN.