In general, what is the widest tyre that you can get away with, on a standard road bike (with dual pivot brakes)?
Edit: I have a Campagnolo Eurus wheelset.
With a bike designed around modern "short-reach" 39-49mm calipers, you're going to four main issues:
1) Brake clearance vertically. If everything else is optimal, a 49mm reach caliper should be able to clear around a 32mm tire. You can verify this with an unmounted brake.
2) Brake clearance horizontally. Extra cable tension releases (e.g. in levers or inline) help with this, but the maximum width that the calipers can spread will not be enough to allow an inflated tire through, and even with a deflated tire you might have to force it.
3) Frame clearance. You'll need to have adequate clearance in three places: seatstay bridge, chainstay bridge, and fork crown. In extremely aerodynamic frames, you also may have issues with seat tube clearance.
4) Rim width of your current wheelset. The Campagnolo Eurus wheelset has a 15mm wide rim. The general rule of thumb is that a tire should be no more than 1.45 to 2.0 times the rim width, which would limit you to roughly 30mm wide tires at the biggest.
In general 23mm should be expected, 25mm is likely, and 28mm is occasionally possible. What actually works on a given short reach frame is going to be heavily dependent on the factors above. Bikes with medium-reach (57mm) or long-reach brakes are more capable; I do road riding on a classic 27"-wheeled Trek refitted for 700c with long-reach brakes, 33.3mm tires and full fenders.
This depends entirely on your frame and your brakes. On a racing frame, you likely won't get over a 25, and some won't fit anything larger than 23s. On a commuter frame with fenders, perhaps 28. Without fenders on something like a Surly, you can easily handle 32s. Assuming your brake calipers can reach around the increased tire width.
Cyclocross bikes are also set up for wider tires, and are often equipped with cantilever brakes to accommodate them.
I've got 28s on my old Euro roadster.