I assume we're talking about a big party here, the sort of event which is fairly casual and where you just drop in, because if it's a very organized event or something small like a dinner party I assume you can find out from your host or hostess about the dress code.

I think when people show up and are obviously dressed wrongly for the occasion, one of two things has happened. (1) They were dressing for the party and completely misjudged the situation. (2) They were dressing for something other than the party i.e. they just stopped by after a fishing trip or they were on their way to the opera but wanted to stop in and say hi.  If you are in a party with a bunch of people you don't know, obviously it is much nicer if they assume you fit into category (2), and within category (2), unless you are really the Robert Redford type of man (I can't really think of an analogue here for women) who wants to get a society girl by saying "why be with one of these fake men when you can come out to my ranch?" I think that nine times out of ten it is much nicer to be going to the opera.  In general, my advice would be to organize your day so that there is a reasonable explanation for why you are dressed the way that you happen to know you look amazingly good and that this reason is not just the party.
 
After all, the nice thing about being obviously wrongly dressed is that it can be a great conversation starter for a situation where you might not obviously have a way to talk about yourself -- this works especially well for women. "I wish I had had time to go home and change," you say to the cute guy at the bar next to you, "but I had to come straight from jury duty, we ran 3 hours over and it nearly came to blows."  Who wouldn't want to hear the rest?

Nice question Virginia.
I would say that for men this is of course simpler as one can easily dress to a middle ground that unless it's a black tie event, or a barbecue, you won't be over or under dressed. If you have to be one of them, mostly I would say it is better to be slightly under dressed than over dressed, but it is more a play on the measure, and mostly depends on your character. Some men would prefer to be grossly over dressed, some grossly under dressed. I am saying this about men, as it is completely different, I think, regarding women. Both of these cases. It is not so easy for women to be on the good middle ground as over and under variants are much more distinct. And the choice of over and under does not depend as much on the character - most women would like to dress as high as reasonable, but obviously don't want to be over dressed as it is stranger for them.

As for your answer Ellen, it is nice and funny, but I disagree with one major premise - that you can talk your way out of it. I would think (not being a woman) that the problem is not so much when someone talks to you, you can assume men wouldn't mind you being way over dressed (or should I say less dressed) but rather it is the gazes across the room. When people simply look at you across the room, you can't really say anything.
Nor does it help to say something. Let's say you come into the party and give your great excuse to everyone - does that help you 10 minutes down the line when you look different than anybody?
Some women might not care about looking different and would prefer the good story, good excuse. You might be one of them (I would say that's not a bad quality to have). Some might even prefer to look differently than others - I'm thinking of Bjork coming to the oscars with a strange swan outfit. But most women I think would prefer to not be overly differently dressed. I am thinking here of women (students) who came to their department in the university over dressed - perhaps they found the extra attention interesting, but never repeated that experiment as it wasn't so nice (with different guys who didn't talk to them before talking all of a sudden to them for a long time etc.).

As for outfits - can't say anything about that.

I find that the most important is to dress appropriately in connection to the activities of the evening, whether you are over dressed or under dressed is then of lesser importance if you’ve chosen the right outfit. For example, if you are going to dance, it usually looks better in a skirt (in pants it is more evident if you’re not a very good dancer), if you are going to a party where that involves any other physical activity, make sure to be comfortable, as being seen uncomfortable is taking away all your inner elegance. I find that if you need to make a speech at a party, it’s better to look over dressed and elegant, and I say it from the side of the on-looker (I’m not at all the type to make speeches so I’m always on the other side).