Jehovah's Witnesses do not celebrate most holidays or events that are common in mainstream Christianity. Examples of some of the celebrations and holidays that Jehovah's Witnesses do not participate in include: Christmas, Easter, Halloween, Thanksgiving, birthdays, and nationalistic holidays.
The reasoning behind why Jehovah's Witnesses don't celebrate many holidays is two-fold. First, there is no scriptural basis for doing so. The Bible does not mandate or even encourage Christians to celebrate any specific holiday. Second, many holidays have pagan origins and/or associations with false religious beliefs. For example, Christmas is celebrated on December 25th in honor of the Roman god Mithras and Easter celebrates the fertility goddess Ishtar.
While Jehovah's Witnesses don't participate in most traditional holidays, they do commemorate two annual events: Memorial of Christ's Death and Kingdom Day (also known as Pentecost). The Memorial of Christ's Death commemorates Jesus' sacrifice for mankind and is held on Nisan 14 according to the Jewish calendar (which falls sometime between late March and late April on the Gregorian calendar used by most people today). Kingdom Day celebrates when Jesus was enthroned as King of God's heavenly kingdom and is held 50 days after the Memorial of Christ's Death on Sivan 6 (again according to the Jewish calendar).