- Cat's tail up in the air with a curl near the tip symbolizes that the cat is in a good mood. This can also symbolize that the cat is loving you and maybe needs a bit of attention, sometimes the curly tail at the tip will come with relaxing purrs from the cat. Another reason for this curly tail at the tip is out of curiosity. If the cat is intrigued and something has got it's attention, you may get that tail up in the air with that curly tip wiggling.
- Tail Wagging or Thumping symbolizes that your cat is just not in a good mood. It is a good idea to just give the cat some space and let it cool off. The harder the thump, the angrier the cat is getting. However, they can also do this when they are happy and engaged in play or hunting. Look for other signs of your cat’s emotions when you see this tail wagging, like growls and hisses. In any case, I wouldn’t get too close.
- Tail down/no movement - Your cat is trying to be low key and probably wants to be left alone. Think of it like a default non-emotional state. Not happy or angry or sad, just mellow. You will see cats do this if they DO NOT want attention (because if it’s up that’s like waving at someone you like, if it’s down that’s like walking by someone with your head down so you don’t have to talk to them).
- Tail curled between legs - You cat is scared. When I take my cat to the vet his tail is curled between his legs the whole time because he is just terrified of the vet.
Conclusion
There are a number of reasons for this and they differ depending upon the situation. When a cat greets a family member (particularly their favorite) the tail is held upright with just the tip kinked over to one side. Don't worry, it's not a permanent kink! This is a sign of safety and familiarity, also used when greeting other animals that are known to the cat.