Roman roads were primarily military, and engineer battalions of the Roman Army normally built them. Cost estimates of road building vary dramatically in different centuries and locations, but it can easily be deduced that they were extremely cost effective. In the first place, building and maintenance costs were ultimately born by local populations rather than by any central Roman treasury: as conquering generals pushed the frontiers outward, they took what they needed locally in cash, kind, and labor and used part of it for road building. Generals were expected to build the roads "out of their own pockets" but those pockets had just been thickly lined with local coin. Money never seemed to matter much in road building -- the locals sweated and paid -- but maintenance fell off, probably for monetary reasons, when the empire stopped expanding and started to slip into decline.
There was a standard plan for Roman roads -- the exemplar was the Via Appia -- but the plan allowed for a lot of flexibility. Aside from money, the variables, much as they are today, were the amount of traffic expected, the weight of expected vehicles, what natural soil or rock structure under the roadbed, and perhaps, most importantly, political clout. A Roman road was complex and multi-layered, but the construction can be summarized in a fairly simple recipe: (1) dig two parallel trenches heaping the material from the trenches into the space between them. (2) Make a shallow 8 to 10 foot wide depression down the length of the heap, and line the edges with curb stones. (3) Line the bottom of the depression first with a layer of 6-8 inch stones set on edge and then with a layer of fist sized stones. (4) Fill in the gaps with "sharp" sand (i.e., not sea or river sand that has grains rounded by water action) and then add another foot or more of sand above the stones -- on later roads the sand and stones might be mixed into a concrete. (4) Pave over with tightly fit big flat stones about 8 inches thick and of the hardest stone that you can find locally. (5) Build unpaved bridle/foot paths along both sides wherever possible.
The central roadbed was normally used for ox drawn wagonry. Horsemen, pedestrians, and marching armies always tried to keep to the side paths that were softer and easier on human and equine legs. In early years, when war chariots were still useful (and that didn't even last into the Empire phase in most areas), they might go short distances on the paved central area. For long hauls, they could be taken apart and, along with all other military supplies, could be put on wagons drawn by oxen. There never was much chariot traffic on any of the roads -- it would be the height of inefficiency and anathema to military commanders -- so the Hollywood images of terrified pedestrians always scattering before charging chariots are pretty much made up. Only in narrow and difficult areas would foot and horse traffic be forced up onto the central roadbed. This might occur on approaches to bridges, gates, and mountain defiles, and that is where you most often see paving stones grooved or "pecked" to provide improved traction for horses and oxen. The Romans had invented the iron horseshoe, but they were tied on rather than nailed and must have been pretty floppy and downright dangerous, both to the horses and to bystanders when the horses ran.
Oxcarts moved at only a few miles per day, but some really quick movements by mounted individuals were possible. Military reinforcements could arrive quickly on roads built parallel the borders, but they probably relied on pre-positioned equipment. Fleeing armies, like Pompey's leaving Rome pursued by Caesar, went as fast on the Roman roads as their officers could drive them. There was a mail service for civilian and military messages, using horse carts -- sometimes covered so the mailmen had a place to sleep at night -- and an even faster "pony express". Rich folks who wanted to travel fast could either preposition horses or conveyances, or trade-in tired horses as they went. But most of what moved went ox-cart slow and for relatively short distances. Roman legions only marched across continents when that was the only way to go -- ships were used wherever it was possible. The same applied to supplies to border areas and to commodities flowing back into Rome. The heaviest traveled roads went from inland to local ports in the provinces and from ports to Rome in Italy.
Roman roads are everywhere around Rome, and the best place to see one near Rome is along the Via Appia in the recently opened National Park that begins just outside Porto San Sebastiano. (Read about it and find Via Appia links at: http://www.mmdtkw.org/VViaAppia.html). Roads, of course, extended right into Rome, and all theoretically started at a big signpost near the end of the rostrum in the Republican Forum -- initially probably at the "umbilicus mundi" at the north end of the rostrum, but later perhaps at a newer signpost near the southern end of the rostrum. Most of the Roman roadwork you can see within the forum is on the pattern of the paved raised central areas of countryside roads and most of it has undoubtedly been reworked many times. A supposedly old section is around the southwest corner of the Temple of Julius Caesar, where the stones are deeply rutted. Another "ancient" segment (also deeply rutted) can be seen from above, just were the Imperial Forum of Nerva plunges under the modern roads. The forum of Nerva was also known as the Forum Transitorium because of that main road that passed through the area connecting the notorious Suburra neighborhood with the Republican Forum.
P.S.: 1) For comparison, the current road system in the United States stretches more than 53 million miles -- one thousand times the size of the Roman system and slightly less than one mile per registered vehicle in the US.
2) For really urgent messages, some system of semaphore or fire signals, passed between signal towers, was used rather than the roads. Nobody really knows how it worked -- it was one of the most closely and successfully guarded secrets of the Roman army -- but messages could apparently cross the breadth of the Empire in a few hours.
2) What about those road ruts? Many human guides and guidebooks will tell you that they were worn into the stones by Roman war chariots. There has also been a long-standing urban legend supposedly linking the standard gauge of railroad tracks to Roman road ruts and the width of the backsides of Roman war-chariot horse teams. More than 2000 Internet sites carry the legend, but it's all bunkum, as both the archeological and railroad communities know. The professionals also know that, while wear may have deepened and broadened some ruts slightly, they were invariably carved into the roads intentionally and by hand to keep traffic going the way it was planned to go. Ruts were carved into narrow sections or through gates like those in the Forum Transitorium or between the famous stepping stones in Pompeii to prevent side-slipping and to keep the wagons "on track". In tight corners, for example at the corner of the Temple of Julius Caesar, carved ruts were curved to nudge the front wheels of four-wheeled carts around: articulated front axles wouldn't be invented until several hundred years after the fall of the Empire. (The lack of articulated front axles was also the real reason that Roman surveyors aimed for strictly straight roads.) Roman roads in the countryside were "high crowned" for drainage, much higher in the middle than at the curbed edges, and ruts were carved into them to keep heavy wagons from sliding toward the edges and tearing up the curb stones when passing in opposite directions. The distance between ruts was essentially irrelevant since the drover would only have to find a rut with wheels on one side to keep his wagon on track. Roman Road Ruts info is contained in http://www.unc.edu/courses/rometech/public/content/transport/Adam_Pawluk/Contruction_and_Makeup_of_.htm. The urban legend is debunked at http://www.railway.org/railroadgauge.htm.