Just as a point of reference with a fairly common rim -I have 32 mm tires on my Mavic Aksium rims. I'm not sure of the width of these rims, but I've run 23's on them. They're not the narrowest ones I have, but they're pretty typical for road rims.

The 32's installed easily, work perfectly, and actually look perfectly normal too. I'm sure I could run a 35 no problem, but dont' care for a tire quite that big.

I can run the 32's at about 60 lbs (I weigh about 165lb). Very rough road and rough pavement and no pinch flats. I might even try 50, but 60 lbs. is comfortable and fast. By the way, I use (IIRC) 19-26mm tubes in there. I tend to like smaller tubes. These, again, work just fine.

Oh, what someone else mentioned - most likely the limiting factor won't be your rims, but the frame and/or brake clearance. The bike I put the 32's on has V brakes (with road levers and Travelagent adapters), so that isn't an issue for me. There's no way I can get anything larger than a 28 (more likely a 25) on my other road bike, regardless of the rims.