What you are looking for is a hybrid tire with not enough tread to be a nuisance and slow you down on the road, but enough tred so that when you go off road you are not losing traction on gravel and mud.
For example Bontrager makes a hybrid tire that is nice: Also, go with the hard wall tires whenever you can.
they cost a little more, but they are more puncture resistant.
So they will cause you less grief on the road.
bicycles.stackexchange.com/users/1473/Chris Belsole
I might suggest you look for a "touring" tire, which I expect is made for reliable long distances on roads including rough roads.
For example I have Schwalbe Marathon Plus tires, and I like them (e.g. for 30 km/day): they are much stronger than my previous tires, and they resist getting flats.
bicycles.stackexchange.com/users/1097/ChrisW
I was looking for something similar to what you are now about six months ago.
I was looking for low rolling resistance, durability and flexibility on a variety of surfaces.
Having used them for this time with one flat caused by a large shard of glass, I'm happy to recommend the 'Panaracer T-Serv PT'.
Details at http://www.panaracer.com/urban.php .
I'm uncertain as to the availability outside this part of the world, but thought I'd let you know anyway.
Good luck!
bicycles.stackexchange.com/users/1492/Jasper Mogg
Knobby treads are really only useful in mud, sand, or snow.
On roads (even rough ones) they just add extra weight and noise.
Of the tires listed so far, the Bontrager and Panaracer tires look like better choices than the NanoRaptor.
I've heard good things about the Schwalbe Big Apple as well.
bicycles.stackexchange.com/users/1047/jefferee
First off, you haven't said what type of bike and size of rim you're riding.
26" tires will not fit on a bike with 700c wheels and vice versa.
Also, if you're riding a road bike you probably won't be able to fit anything bigger than a 700x25 or 700x28 on it
and you almost certainly won't be able to get anything with much tread on it.
That said, get the largest tire you can get on your frame.
It'll slow you down a bit on the road, but it'll speed you up a lot on the rough patches and smooth out your ride as well.
As far as the tread goes, I would look for something with a good number of large knobs on it that are fairly close together.
Too much tread
and you'll feel it on the road, too little and you'll be slipping around on the pitted and rocky patches.
I don't have experience with this particular tire, but this is what I mean by large knobs that are fairly close together: http://www.google.com/products/catalog?q=hybrid+bicycle+tires&hl=en&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&biw=1024&bih=655&um=1&ie=UTF-8&tbm=shop&cid=7981081227657122988&sa=X&ei=gsLoT4WcN-Ps2gXlwOSJCw&ved=0CKoBEPMCMAk4Cg
bicycles.stackexchange.com/users/4239/jimchristie
The WTB NanoRaptor (looks like it's now just the "Nano") is one of the more popular MTB tires with pavement performance in mind.
It's more off road oriented than the tires that Stopher87 suggests, but still has a nearly continuous center bead that makes it roll smoothly on asphalt.
It may work better for you on loose gravel roads.
Here is the 29er version: http://www.wtb.com/products/tires/29er/nano-29er/
bicycles.stackexchange.com/users/1166/Russ
My tires are worn out so I want to change them.   When I am trying to change them, I want them to be to the best fit for the conditions I cycle in. I cycle about 30 km a day on roads ranging from smooth pitched roads to very rough roads consisting of pits and stones in the most haphazard way.   Please suggest a type of tire that would be best for me. There do not need to be considerations for snow, it does not snow where I cycle.
Which tires are best for on and off road use?
bicycles.stackexchange.com
<tire>
bicycles.stackexchange.com/questions/3768
bicycles.stackexchange.com/users/847/Starx
For riding on and off road what is required is a hybrid tire with not enough tread to be a nuisance and slow you down on the road, but enough tread so that when you go off road you are not losing traction on gravel and mud.   The market has a number of such tires available, including Bontrager hybrid tire, Panaracer T-Serv PT and Schwalbe Big Apple Hybrid or touring tyres with a solid wall and close knobbly tyres provide the best compromise between grip and speed. Good brands include Bontrager, Panaracer T-Serv PT, NanoRaptor and the Schwalbe Big Apple.
Hybrid and touring tyres provide the best compromise between grip and speed. Tyres with a hard wall and close knobbly treads are good. Some examples of good brands include Bontrager, Panaracer T-Serv PT, NanoRaptor and the Schwalbe Big Apple.