For one thing, I tend not to tell people how old I am when I explain my job to them.
Generally I try to break it down to some sort of brief explanation of what I'm responsible for doing - you didn't get asked "how do you do your job?", you got asked "what do you do at your job?". I tend to explain it something like this:
Basically, I'm responsible for building the parts of a website that make it 'interactive'. So if you came to us and said "I want a website that makes toast when I click on a button", someone else would design it - but I would be the one in charge of hooking up the toaster and making sure that when you clicked that button, the toast got made.
So far, that explanation has served me pretty well.
If someone also happens to do the same, they'll often ask a few questions and you can happily geek out together. More often than not, the response is more along the lines of "I hate computers." To which my answer is: "I understand."
While computers are not the enigmatic beast they used to be, for most people they are a necessary evil. You don't want to be seen as an emissary of that evil, but rather a soldier on the front lines.
It depends who am I talking to. Most of my users I choose to run with with:
Come to me, user! I defy you! Come and kneel before Zod! Zod!
If it's family or friends of family I try and underemphasis the "I work with computers" because, from lessons learned, the recipient almost always hears "I work on computers; please bring your computer woes to me and your pittance of change and harass me for ever because you are 'doing me a favor' and could totally do it yourself but don't have the time".
If I am talking with a broad at the bar I tend to explain my job as such: "Information manager... but it's really boring and not much fun. What do you do?".
I just say I make websites. Most of the time when someone asks what you do, they just want to know what happens on the surface, they don't care about the specifics of your day to day routine unless they are in the same field or if you happen to work on a really interesting field and web developer is not one of those interesting fields to an outsider.
I tend to test the waters on occasion to get a feel for how savvy the client is with a joke, such as saying I use black magic to make my websites work. If they stare and marvel and want to see magic I drop the client before my sanity drops.