I am one who is very open about our adoption. My case may be different (as a PP stated) since I adopted through the foster care system. I took my cues from my kids. They became very comfortable letting people know that they were in foster care and then celebrating their adoption (since it took almost 3 years to get from placement to finalization they/we had a lot of supportive friends, classmates, etc.), so we are all very open about it. I, personally, felt that there could be nothing wrong with being open and honest. My kids know that they are just as much loved and cherished as my bio son is and are treated no differently.
There was also the issue of school stuff -family trees, family history, pictures, etc. My kids teachers were grateful to be aware of the kids' situations so that they could be sensitive in these cases. I th ink I was far more worried about it than my kids were!
To the OP: you have to do what feels right for your family. I am so proud of the fact that I grew my family through adoption that I will talk about it to whomever will listen! LOL I find that (so far!) I have not run into anyone who looks at adoption as anything other than positive.
Good luck!