I was going to say One Piece, as it's my favorite anime, but then again it's popular enough that quite a few people are familiar with it already. I'm thinking Terra e... would be a better choice, as it's nearly as brilliant and much less popular.
If it was just one anime, all the way through, it'd be hard to say.
I mean, each anime is so diverse in its themes, it's just not possible to have one anime cover them all. On top of that, some really good anime might have a bad effect on people's outlook on anime. Furthermore, each anime has its own appeals, so it would be difficult to choose an anime for such a wide audience to view.
But under these circumstances, I suppose I would have to choose a well balanced anime, that has its own share of action and drama, and though it's not my favourite anime it's definately one of my favourites and with the ability to apply to a large audience.
So, my top choice would be Planetes. Though, given enough thought, I might switch to an anime with a hefty animation budget, since pretty things tend to draw people more than overall good stories (despite that being one of the major selling points of most anime).
Interestingly enough, looking over the thread a lot of the listed anime I've never seen or is in my top 20... perhaps I should add a couple of these to ptw.
In top 20:
Welcome to the NHK
Honey and Clover
and Code Geass...
Since it's not exactly a "whats your favorite anime" thing...
I think everyone would benefit from seeing kino's journey. And if you consider spreading a bit of insanity around the world to be good thing, then NGE definently.
Ouran High School Host Club. I know a lot of different people who have seen it (Girly girls, manly men, etc) and they all like it. I even know people who do not watch anime regularly (or don't watch anime at all) who liked it.
I'm gonna have to go with The Vision of Escaflowne. it's one of the great anime titles of the 90's. which is saying a lot since that decade featured a lot of amazing shows. Escaflowne manages to appeal to a wide audience because it overlaps several genres. action, fantasy, and throw a little bit of romance as well.
Asako said: GTO, probably. It's a timeless classic comedy.
if only we didn't have to pick one, this'll be one of my other choices.