Well, it depends a lot on the specific model of bike, and likely even on the exact frame size.
You can probably eyeball it to get a good idea.
Remember that larger tires are both wider and stick out more from the wheel.
On a road bike, odds are high that you can put a slightly larger (say, go from 25mm to 30mm) tire but not a hugely larger tire.
If you want to make a big jump you probably also want to get wheels with a wider rim.
Note that for off-road tires, the knobs aren't usually counted in the mm size but definitely do affect whether or not the tires fit on your bike.
Look for: Front and rear:
Brake clearance — can a larger tire fit in the brakes?
If this is the only issue, you can get different brakes
Rear:
Stay width — will a wider tire rub on any of the stays (rear)?
Rear:
Stay bridge clearance* —
will a larger tire hit the bridge between seat stays or chain stays?
Rear: Seat tube clearance —
many bikes have a geometry where too large of a wheel/tire will hit the seat tube above the cranks Front: Fork clearance — how much room is there under the fork crown?
(height and width)
Front:
Down tube clearance — how much extra room before the front tire hits the downtube?
bicycles.stackexchange.com/users/76/freiheit
Road frames come in a wide variety of styles, so it's impossible to give an exact answer without knowing more about your bike.
Also keep in mind that wider tires also have a larger diameter, so your bike has to have enough clearance for both.
A typical modern road bike with caliper brakes is going to have very tight tolerances: many will max out at a 28mm tire, some at only 25mm.
When mine was built, I had the frame customized and used long reach brakes just to allow 28mm tires plus fenders --
even then it's a tight fit.
Another problem with calipers and wide tires is that you may not have enough brake cable slack to remove the wheel easily (I have to deflate mine slightly to get the tire past the brake shoes).
Touring and cyclocross frames tend to be built with much more generous proportions and have room for bigger tires.
Using cantilever brakes also helps give much more tire clearance vs. calipers.
My last touring frame used 32mm tires and could have easily gone up to at least 35mm, if not bigger.
If you're putting on much larger tires, you should also consider larger rims (see Sheldon Brown's tire/rim sizing chart ).
Using a big tire on too small a rim is a recipe for trouble.
Plus a wider rim adds more strength.
So you may need a wheel rebuild to make this happen.
bicycles.stackexchange.com/users/157/darkcanuck
If your bike has 700C wheels, you could convert to 650B.
The wheel radius is only 25mm less, so most things work the same, but you have that much more room for tires and fenders.
You'll probably need to replace your brakes with long-reach brakes.
bicycles.stackexchange.com/users/605/Jay Bazuzi
In the eight years since this question was written, road-style bikes with fatter, grippier tyres for off-road use have become pretty common.
They're usually called "gravel bikes" or "adventure bikes".
Plenty of companies are making bikes of this type: essentially, a relaxed-geometry road-ish frame with enough tyre clearance for something like 40mm tyres for use on ground that's, say, as rough as a hiking trail but not so rough that you'd need a mountain bike.
bicycles.stackexchange.com/users/13174/David Richerby
I have a Norco Search 2017 Sora and actually has 700x38C tires (B'Twin tires).
It came originally with Schwalbe Road Cruiser 700x32c K-Guard.
So, it depends what are the height and width of the fork.
bicycles.stackexchange.com/users/32384/Ronald
For our small expedition with our bicycles in Patagonia we invested into slightly larger tires and more durable ones (we choose the Schwalbe Marathon XR in 700C, the widest our bike frame could accomodate).
It did quite a change, you hear more the tire noises, it helps better in muddy terrain and feels more confortable in gravel roads or in the fields.
However, it's not really good in sandy parts or when the gravels are too big or too loose.
Overall it was a good and needed change, it would have been much less confortable to ride down in Patagonia with out those wider tires.
If you decide to change yours, follow freiheit advice or go pay a visit to a local bicycle shop.
It's not always possible to put different tires because of the rim, brakes or frame.
bicycles.stackexchange.com/users/748/Huygens
I am curious if anyone has put larger tires (mountainish) on their road bike.  I am thinking about doing this to do some riding on gravel roads/touring/commuting from rural areas.  I have an older steel Norco.  How rough can I ride this with bigger tires without damaging the bike?  (Purely just for curiosity.  I am not planning on doing any drops etc but if I drop off a curb now and then does that matter?)
Larger tires on a road bike
bicycles.stackexchange.com
<tire><road-bike>
bicycles.stackexchange.com/questions/1886
bicycles.stackexchange.com/users/134/sixtyfootersdude
It is not always possible to put mountain bike wheels on a road bike because of the rim, brakes and frame. It depends on the bike. To find out if this change can be done, follow the advice on freiheit or pay a visit to your local bike shop.  Determining tire size, and whether you could use larger tires at all, may depend on the bike's model, as well as on specific parameters like the rim, brakes and frame. On an average road bike there is little leeway for larger tires, and the effect of a tire change is not great. If the change is performed, it is best to have it done by a professional.
Determining tire size, and whether you could use larger tires at all, may depend on the bike's model, as well as on specific parameters like the rim, brakes and frame. On an average road bike there is little leeway for larger tires, and the effect of a tire change is not great. If the change is performed, it is best to have it done by a professional.