Neglect, omit, disregard, ignore, overlook, slight, forget are comparable when they mean to pass over something without giving it due or sufficient attention.
Neglect usually implies intentional or unintentional failure to give full or proper attention, especially to something one is doing (as a task) or should do (as a duty) or to someone who has a claim upon one's care or attention.
Omit implies a leaving out of something which forms a part of a whole or a neglecting entirely through oversight, inattention, or absorption of an important detail, opportunity, or aspect.
Disregard usually implies voluntary, sometimes deliberate, inattention; the term may or may not imply justifiable neglect.
Ignore usually implies either an intention to disregard or a failure to regard something more or less obvious; it may even suggest a deliberate closing of the eyes to what one does not wish to recognize.
Overlook implies an omitting or disregarding, sometimes through intention but more often through haste, or lack of care.
Slight may imply neglect, omission, or disregard, but it also usually implies a contemptuous or an arrogant attitude that makes one undervalue a thing's importance, treat a person disdainfully, or be neglectful in performance of a task or duty.
Forget (compare FORGETFUL ) often retains in this relation the implication of losing the memory of something or someone, so that when it implies neglect, it usually carries a suggestion of willful ignoring or of a failure to impress the thing neglected upon one's mind.