January 1831: The Best Friend of Charleston begins operation on the South Carolina Railroad

First entirely American-made locomotive in revenue service on an American railroad

Manufactured 1830 by the West Point Foundry, Cold Springs, Harbor, N.Y. for the
South Carolina Canal and Railroad Company. Dissambled and shipped by boat to Charleston in Aug. 1829. Begins operation on first six miles of the line.

Destroyed by a boiler explosion June 17, 1831 (first such event in U.S. history)

"The blast is said to have been caused by the fireman tying down the steam pressure release valve; he had tired of listening to it whistle, so to stop the noise he closed the valve permanently (another account has the fireman placing a stout piece of lumber on the safety valve and sitting on it). The blocked valve caused the pressure within the boiler to exceed its capacity, and it exploded. The resulting blast was said to have hurled metal fragments over a wide area and killed the fireman." 

line drawing of the Best Friend of Charleston .(source)

Eventual 136-mile route of the Railroad.

"With the advent of cotton cultivation in the early 19th century, the relatively remote South Carolina upcountry enjoyed a vast expansion in the value of its agricultural produce. Overland transport by wagon was slow and expensive, so this produce tended to go to Augusta, Georgia, then down the Savannah River to the seaport at Savannah, Georgia. The SCC&RR Company was chartered on December 19, 1827 (amended January 30, 1828) to divert this commerce to Charleston by means of connections to Columbia, Camden and Hamburg. Despite its novelty the project was pursued by its Charleston leaders with aggressive method, public demonstrations encouraging support for the daring concept of a steam-driven railroad. Under William Aiken as the first president, six miles  of line were completed at Charleston in 1830. The first run over the entire 136-mile line was celebrated in October 1833." 

related:

1831 Morris Canal completed between the Delaware River and Newark. (extended to Jersey City in 1836). WP: "It was considered an ingenious technological marvel for its water-driven inclined planes to cross the northern New Jersey hills."

1831 Chesapeake and Ohio Canal begins operation. "C&O Canal and occasionally called the "Grand Old Ditch," operated along the Potomac River from Washington, D.C., to Cumberland, Maryland. The canal's principal cargo was coal from the Allegheny Mountains.

1830 Baltimore & Ohio railroad begins operation on first section, from Baltimore to Endicott Mills, Maryland. (May 24).  The B & O's locomotive Tom Thumb races a horse-drawn car (Aug 28).

Tom Thumb was the first American-built steam locomotive to operate on a common-carrier railroad. Designed and constructed by Peter Cooper in 1830, it was built to convince owners of the newly formed Baltimore and Ohio Railroad (B&O) to use steam engines and not intended to enter revenue service. It is especially remembered as a participant in an impromptu race with a horse-drawn car, which the horse won after Tom Thumb suffered a mechanical failure. However, the demonstration was successful; and in the following year, the railroad committed to the use of steam locomotion and held trials for a working engine." (source)

1830 New Jersey charters the Camden and Amboy Rail Road (February 4).  Begins operation in 1832.

1829 Stourbridge Lion  (British-made) becomes first steam locomotive to run on rails in the U.S., in Honesdale, Pennsylvania, for the Delaware & Hudson Canal Co. (Aug. 8)

Depiction of the first run of the locomotive Stourbridge Lion  Painted c. 1916.  (source)

1830 Massachusetts grants charter to the Boston and Lowell Railroad (June 5). Begins operation 1835.
1828 Horatio Allen of the Delaware & Hudson Canal Co. tours England with intention of buying a steam locomotive, acquires Stourbridge Lion from Foster, Rastrick and Company.
1828 Delaware & Hudson Canal open to navigation
1827 South Carolina Canal and Railroad Co. is chartered by South Carolina (Dec. 19).
1827 Maryland charters the Baltimore & Ohio (Feb. 28), followed  by Virginia (March 8), with the task of building a railroad from the Port of Baltimore over the Appalachians to the Ohio River. B & O is incorporated on Apr. 24 with initial capitalization of three million dollars of stock.

"The fast-growing port city of Baltimore, Maryland faced economic stagnation unless it opened routes to the western states, as New York had done with the Erie Canal in 1820. In 1827, twenty-five merchants and bankers studied the best means of restoring "that portion of the Western trade which has recently been diverted from it by the introduction of steam navigation." Their answer was to build a railroad—one of the first commercial lines in the world."

1826 Hudson & Mohawk Railroad is chartered by New York (Apr. 27).

Construction began Aug. 1830, with the intention of linking the Mohawk River at Schenectady with the Hudson River at Albany. It was conceived as a means of allowing Erie Canal passengers to quickly bypass the circuitous Cohoes Falls via steam powered trains

1826 Construction begins on the Pennsylvania Main Line of Public Works, a hybrid railroad and canal navigation system to connect Philadelphia with Pittsburgh. Rail portions authorized by the Pennsylvania Legislature in 1828.
1826 The Granite Railway (horse-drawn) is chartered in Massachusetts (Mar 4), built to carry granite from Quincy to a dock on the Neponset River in Milton. Begins operation (October 7).
1825 Erie Canal opens to navigation (October)
1825 John Stevens of Hoboken, N.J. builds a locomotive and runs it on his summer estate.
1825 Construction begins on Delaware & Hudson Canal (Jul. 13)
1824 New Jersey Charters the Morris Canal and Banking Company to construct a water navigation system from the Delaware River to Jersey City on the Hudson (Dec 31) .
1823 Delaware & Hudson Canal Company is charted by New York to to build and operate canals between New York City and the coal fields around Carbondale, Pennsylvania.
1817 Construction begins on the Erie Canal

1815 New Jersey issues first corporate charter for a railroad in U.S., to the New Jersey Railroad Company on behalf of John Stevens and others, for a railroad between New Brunswick, N.J. and Trenton (February 6)

1813 Oliver Evans proposes a steam railway between New York and Philadelphia [ref]
1812 Documents tending to prove the superior advantages of rail-ways and steam carriages over canal navigation, John Stevens, cited as the "birth certificate of all railroads in the U.S." [ref] 

1808 U.S. Treasury Sec. Albert Gallatin issues report on federal funding of roads and canals
1806 U.S. Congress authorizes funding for replacement of the Braddock Road (eventually called the Cumberland Road)

1804 - Penydarren or "Pen-y-Darren" World's first steam locomotive railway constructed in Wales by  Richard Trevithick, used to haul iron from Merthyr Tydfil to Abercynon, Wales.  

1800 British patent expires on Boulton and Watt steam engine, "permitting others to build high pressure engines with high power to weight ratios, suitable for locomotives."

1795 Bridge over the Hackensack River creates uninterrupted toll road between the Jersey City and Newark.

1795 Philadelphia to Lancaster toll road opens as the first road in the U.S. using modern engineering and construction techniques.

(dot.gov)  : "The privately built Philadelphia and Lancaster Turnpike Road was the first important turnpike and the first long-distance broken-stone and gravel surface built in America according to formal plans and specifications. The road's construction marked the beginning of organized road improvement after the long period of economic confusion following the American Revolution."

1792 Pennsylvania issues charter for turnpike from Philadelphia to Lancaster
1790 New Jersey issues charter for a public toll road between Jersey City and Newark

1789 C. Colles issues the first comprehensive road maps of the United States

1785 Christopher Colles submits plan to New York legislature for a canal to connect the Hudson River to Lake Ontario

"...a plan to improve the waterways of the Mohawk Valley in New York. In his pamphlet entitled the Proposal for the Speedy Settlement of the Waste and Unappropriated Lands on the Western Frontiers of the State of New York, Colles proposed that a series of canals and locks be constructed along the Mohawk River and Wood Creek that once completed, would connect the Hudson River and Lake Ontario, effectively uniting by water passage the Atlantic Ocean to the interior of North America"

1780 British Army under Henry Clinton invades South Carolina, laying siege to Charleston (May 29). Siege is broken with 5000 Americans taken prisoner (May 12). British Army begins advancing through the Carolinas towards Virginia as part of the "Southern Strategy" to break resistance of the colonies. They rout the Americans under Gates at Camden, S.C. (Aug. 16). "The rout was a humiliating defeat for Gates, the American general best known for commanding the Americans at the British defeat of Saratoga, whose army had possessed a large numerical superiority over the British force. Following the battle, he never held a field command again. His political connections, however, helped him avoid inquiries and courts martial into the debacle."

1755 Braddock Road opened as first land route from the Chesapeake basin over the ridge of the Appalachians to the Ohio Country. Built by British Army troops and Virginia militia.

(source) Route from present-day Cumberland, Maryland (on the Potomac River) to vicinity present-day McKeesport, Pa., near the confluence of the Monongahela and Youghiogheny rivers, where Braddock was killed.

In 1755, Braddock was sent to remove the French from Fort Duquesne (present-day Pittsburgh) Starting from Fort Cumberland, General Braddock ordered 600 men, commanded by Major Chapman and John St. Clair to cut a military road over Haystack Mountain. The road followed an Indian path known as Nemacolin's path which had been improved by George Washington and Christopher Gist for the Ohio Company. Compton's task was to build the road to Little Meadows, about 20 miles away.
After a day of road-building, Maj. Chapman's men had only built two miles of road and had destroyed three wagons trying to get over the treacherous terrain encountered on the mountain. Braddock was about to dispatch 300 more men to the road crew when he was informed, by Lt. Spendlowe of the Navy detachment, of an easier route through the Narrows.
Braddock took approximately 1400 men, with accompanying wagons, along Spendlow's route and joined Chapman's road at Spendlow's Camp, in today's LaVale, MD.

Braddock met defeat east of Fort Duquesne and was fatally wounded ^{(at the Battle of the Monogahelia on Jul. 9)} He was buried in the middle of the road he built, and his soldiers marched over the grave, with the hope of concealing the grave's location from the Indians. The grave was found years later by road workers and the grave was moved. The site is now marked by a marble monument erected in 1913.
The Forbes Expedition, a more successful British expedition mounted against Fort Duquesne in 1758, used a different route through the mountains west of Carlisle, Pennsylvania along what became known as Forbes' Road.

1750 Douwe's Ferry Road is completed between the Passaic River and the Hudson in New Jersey