Town Plan Boards
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This will cover specifically North American town plan boards, as trying to account for the dizzying number of European variants that I have no expertise in would be, well, dizzying.
Rather, as with most of the archive, we're going to stay self contained.
1961-1967 Town Plan Boards
The first boards were available via two sources: the 725 Town Plan or the 246 supplement(which is just the board by itself). It sold for $1.50 in both the USA and Canada starting in 1961(Canada is included as because the full line of sets and supplements were mentioned in several 1961 sources(ie The Hamilton Spectator, November 24th, 1961), it's likely the 246 supplement was available as well).
It first appeared in a 1961 brochure(V1867), only as a mockup using the European town plan's image/layout:

In the finalized version, there are two variants. The earliest has a cloth hinge:
And the later version with a stronger paper hinge:
Also generally expect the printed layout to shift a bit, as it's a bit inconsistent between examples on all the sides.
The cloth one came first as it omits the patent information below the logos(as does everything designed in 1961). My guess is about 1961-1963 when this version was available, as it seems about as common as the later version.
In the image below, the top is the cloth hinge and the bottom is the paper hinge version:
It's very likely that the hinge redesign prompted the update to include the patents.
The other side has the same image as featured on the top of the box and never updated/changed(paper left, cloth right):
The 246 and the 725 Town Plan retired in 1965 in the USA and in Canada. The 246 was available in Canada until ~1967.
The 842 Town Plan Board
The 842 Town Plan first appears at Sears as an exclusive set in late 1969:

It continued sale into late 1970, making a very sneaky appearance but still identifiable by its piece count:

Despite this, the set and consequently the board are increasingly rare. The limited availability of the set is a large cause of that, but the lack of any LEGO branding whatsoever leads it to be commonly separated(I found mine in a lot of Hot Wheels, meaning there is an 842 somewhere out there without its board):
The back is completely blank with no designs:
It is one of the last town plan boards ever used in the LEGO System.