I do grow the rose ('real' name Rosa eglanteria.)
It is a great rose and also had the good sense to survive last years severe Easter Freeze with almost no damage.
The galls you see are the result of a wasp laying eggs. The slightly spiny galls that result have a larva growing in each one. Pruning them off will reduce the number next year (and too many aren't good for the rose.) Generally the galls are either 'mossy' or 'spiny'.

Here is a link that might be useful: The two main kinds

That's interesting. They mostly go after the hips here and leave the stems alone. They do chomp on gallicas. I grow the Sweetbriar, too. We look out the window at night, and there they are, going after the hips.
They leave alba semi-plena alone, and Madame Hardy alone. Felicite Parmentier.
Come to think of it, I have always been puzzled why Harison's Yellow stays so short around here.
I shall have to go check this out.
They won't leave my Crimson King maple alone. It's a sixteen year old bush.
Hmm. I also have a common moss which never gets tall. i've owned it for several years, but never seen a bloom.

Mersiepoo, I used to live in Pennsylvania myself, and grew sweetbriar (or eglantine) when I lived there. Mine also had the galls. I did not at the time know what caused them. I did just what you are being advised to do, which is to prune them off as they occur.

The scent is marvelous, isn't it?

Rosefolly

I've seen a leaf gall and a stem gall on the naturalized Sweet Brier out here. It's thought that the gall wasps were accidentally imported with the Sweet Brier. They aren't terribly harmful, as they aren't crown galls or bud galls and won't affect flower. You'll see a lot of careless identification online, with a lot of different galls all given the same name. My distinct impression is that the gall-causing wasps are quite specific as to the hosts they favor. There are definitely problems with a couple of gall-causing wasps invading garden roses in Canada, but they aren't wasps that favor Sweet Brier. One of the great experts is Dr. J.D. Shorthouse, who has written at length about the various species of gall wasps and the assorted insects that parasitize them.

Here is a link that might be useful: Gallery of Rose galls

Thank you everyone for your replies! :) I noticed that there were some REALLY weird galls (they looked like mouse brains, no kidding!) on a cedar that I have as well. I clipped them off of all the plants (including the cedar). I didn't get many flowers this year :( but at least the bush is still alive. :) It's growing pretty well so far, I don't think the galls really hurt it, but I will make sure to prune them off if they appear again this year.

I never noticed galls on my other 'stick' roses, btw. Thanks for the info and the links, everyone!

Sweetbriar rose is also a weed in some parts of the country.

It was my understanding that Sweet Briar is Rosa rubiginosa. Whatever its Latin name is, has anyone noticed that the foilage (and perhaps the hips) have a very sweet smell in the middle of winter when the weather is damp? I wouldn't call it an apple like smell but it is very strong.