There are many reasons why an employee might need (or want) time off work. Unfortunately, not all of them are legally protected. Although larger employers must let employees take FMLA leave, no law requires employers to offer paid vacation time or personal days. Except in a few places, employers generally don't have to offer paid sick leave, either.
That doesn't mean no legal rules apply in this area, however. Employers who choose to offer sick or vacation time (or to combine them into PTO) must meet some legal requirements. Employers may also be legally obligated to give employees time off for certain obligations of citizenship, such as voting and serving on a jury. The law also provides strong protections for employees who need time off for military service.