I cannot stand to hear "his/her", a result of Women's Lib. I still contend that, although we use it, "their" in this case is not the best, as there is a great argument for the lack of agreement of number. Therefor, I always try to avoid the mess, especially in formal writing, by changing the structure to something like: "We all have our dream(s)".
For what it's worth, there's at least one American here who's fine with "Everyone has their dream." If it was good enough for Bill Shakespeare, it's good enough for me. Zounds!
Of course, if the construction were "every one of us has ...," I would expect to then hear "his" or "her" and not "their."
Although sexism does exist in the world, I believe it is out of convenience, and not sexism that the default pronoun gender is masculine when you don't know whether the acting party is a him or a her. It's acceptable, except for those who believe that it is out of sexism (that the default gender is masculine)! As stated above and shown in other posts, if you do not take the default gender you are left with creating all sorts of machinations in writing to satisfy all parties.
