I guess part of what we are disagreeing about, or perhaps just talking past each other on, is whether it is appropriate to single out jeans (absent, of course, some venue rule) -- or anything else the hosts don't happen to want. Why not then "no jeans, shorts, flip-flops, tank tops, graphic tees, goth wear, revealing clothing, etc., etc., etc.? (From what we read about here, it wouldn't surprise me!

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That is, several posters are trying to think of the best way to express "casual but no jeans." And I don't think you really can properly do that. You just write "casual" or "dressy casual" (I have long ago given up objecting to that one). If nice jeans are not appropriate "nice casual" wear in your community, most people will know that. If that's not the standard, then what's the point of specifically directing people not to wear them? To me, it's almost like saying "no orange" or "no vulgar jewelry" or "no colors that will clash with the color scheme." "No jeans" isn't a dress code standard (maybe for a school, but not for an invitation).
Yes, Cat-Fu, you're right, I didn't mean to say that it's rude to include dress code on an invitation. It's perfectly correct (and, speaking for myself, much appreciated).
But there is a big difference between putting a dress code such as one of the standard (black tie, white tie, black tie optional (also one I've given up on!), dressy, casual, dressy casual, business, casual business, costume) or at least easily understandable and specific to the venue or activity (beach attire, pool attire, ski attire, boating shoes), and dictating exactly how the guests are supposed to conform to the standard.
The first gives the guests information on how dressy the event is, information they need to know and can only get from the hosts. The second tells them you don't trust them to understand the standard or to dress appropriately, insulting their manners and/or their intelligence.
That many guest lists include people who refuse to dress properly doesn't change the duty of the hosts to be polite on their invitation any more than it would excuse including a note with guidelines about proper table etiquette. Those guests probably won't cooperate anyway! And it's no excuse to insult all the others. You just have to hope for the best and then forget it.
Everyone seems to be commenting on the jeans part. What do you think about the "no ties" part?