This is a common question, but it's not very good accepted in some places, from some people. There are different ages, in fact: passport age (ID card age; calendar age), biological age, psychological age. Most of the people ask (and know) only the first one.
OK, strictly ontopic: if you are asked your age in a context in which a/ you cannot respond offensively/rudely, b/ cannot just keep silent and c/ you should not respond honestly, there are many polite, humorous, good ways to respond to this question without causing offense and maintaining your privacy.
Here are some ideas:
- "How much will you donate to my favourite charity, if I tell you?"
- "It’s over 100 already. I'm immortal."
- "I'm old, but... what we lose in form we gain in wisdom."
- "Look, even my closest friends don't ask me how old am I."
- "I’m so old that I've forgotten."
- "Well, old enough to vote."
- "I'm just a little bit older than my teeth."
- (How old are you?) "I'm not old at all."