Remember when you first started studying Chinese? The teacher always made you introduce yourself. It usually consisted of something like the following:
My name is…
I am from …
I am … years old.
It's all very cute and practical, and instinctively seems appropriate to both beginners in a language as well as three-year-old native speakers. This type of basic self-introduction is generally accepted as normal and necessary.
Unfortunately, this self-introduction (自我介绍 in Chinese) often goes un-updated for years on end. So you've been studying Chinese for 2 years, are at a solid intermediate level, and yet you basically still recite the same self-introduction above (perhaps swapping out your age for your job). That's kinda lame.
In reality, every new word you learn, every cool new grammar point, could potentially enhance your stale old self-introduction. Take the time to do the upgrade! Just like failing to upgrade your 听不懂 is going to affect your interactions with Chinese people, failing to upgrade your self-introduction will have the same effect. Ideally, your self-introduction should be as cutting-edge, language-wise, as you can smoothly handle. It's OK to show off your Chinese level with your self-introduction just a little, if it means people will stop treating you like you just learned to say 你好.
The nice thing about self-introductions is that you can be creative. Keeping in mind that this is going to vary a lot depending on the individual, the audience, and the Chinese level of the speaker, here are a few suggestions to get you going:
If you have a Chinese name, and you tell your audience which characters are used to write it, use creative, interesting choices of words that use the characters in your name. You can use this trick to associate your name with a famous Chinese person you're a fan of, or whatever you can come up with.
As you tell your audience where you are from, use the opportunity to stifle annoying stereotypes from the beginning (e.g. "I'm an American but I've never owned a gun," or "I'm French but I'm not at all romantic," etc.).
Add in your Chinese zodiac sign instead of your age for fun (and to show that you're not a total newb in this whole "Chinese culture" game).
Depending on the audience, you may want to head off other annoying questions, by saying things like "I can use chopsticks" or "I am used to eating Chinese food", but make sure that it comes across as a joke, and not the lamest brag ever.
Include a few details about why you first came to China or why you haven't left yet, after all these years (because the Chinese are already curious about that kind of thing)… but be prepared for follow-up questions!
Include what Chinese movies, books, or dishes you like for a chance to make an instant connection with certain members of your audience.