Some do and some don’t. I think most Jews observe Thanksgiving the same way most Americans do. They take the day off from work and use it as a time to gather with their family. In addition, they may offer a word of thanks to God for what they have, although not as a religious holiday per se.
Some Jews do not observe it since it is not really a Jewish custom. And anyway we are obligated to give thanks to God every day of the year.
Interestingly enough, Thanksgiving has "Jewish" roots. The Pilgrims based Thanksgiving on the Torah (Bible), in which God commands Jews to celebrate the Harvest Festival. This festival is called Succot, the Festival of Booths, which Jews have been celebrating for more than 3,000 years.
And, allow me to add a fairly well-known clever comment: The word for “thanks” in Hebrew is “hodu” which also is the modern-Hebrew word for turkey! (There is a verse from Psalms that we says during prayers, “Give thanks (Hodu) to God, for He is good, for His mercy is forever (Psalm 136).”
