of small towns and villages a bit over 100 years ago.
"New Utrecht Avenue" runs through Borough Park and Bensonhurst, which seems to have been built to contain an elevated railroad (the W train today). More or less parallel to it, and several blocks east, there are traces of "Old New Utrecht Road". A few blocks of it exist, and there are other properties that clearly used to border it, because they have strange diagonal sides. There was a short row of 3 houses that were knocked down and replaced recently, at the intersection of 16th Ave and 43rd St., which had fronted on Old New Utrecht Road. They had been diagonal to the grid, and set back somewhat from the corner, such that there was a triangle of open space in front of them. One could see (although not any more) the diagonal backs of buildings on adjoining blocks that followed the same line as the vanished street.
See http://www.forgotten-ny.com/Alleys/utrecht/utrecht.html for a fuller treatment.
In my neighborhood, today called Midwood, there are 3 or 4 parallel streets at an angle to the current street grid: Elm Ave, Roder Ave, Ryder Ave, Locust Ave, Cedar Ave., and more or less at right angles to them, Bay Ave. There's about 1/2 block of Bay Ave. extant, and more of it is visible in the property lines of buildings where it used to be. Cedar Ave. is disappearing - part of it is a parking lot, one block of street still exists. According to old maps, these were the streets of South Greenfield.
Railway lines can be traced, but with difficulty. For many years, there were two parallel, competing railroad lines running between East 15th and East 16th Streets, from Avenue H (the LIRR Bay Ridge Branch) to the Coney Island beach. In 1924, the line owned by the LIRR was torn up, and the land sold off for housing. But at each street crossing (the lines were are on an embankment), there is still a pair of double-length abutments, showing where the old line used to be supported, even though houses now fill in the space where the old line had been.
Broadway, in Manhattan, probably would have been such a street, and Thomas Randel, the designer of the Manhattan street grid, wanted to get rid of it, but as it developed, Broadway remains, twisting across the city.