The 1965 TV series "F Troop" had a very  unique logo which was a prime example
a very unique style of illustration which was very popular in the last
half of the 1960s, but seems to have quickly gone out of style.  If
you remember the opening of the show, there was first a wide shot of
the logo, in which the stylized words "F Troop" framed a central
drawing. The drawing
illustrated many scenes from the series: the reville cannon blowing
down the watchtower, etc. The cartoon drawing was very complex, deeply
packed with these individual vignettes; the camera would focus on
individual scenes during the show's opening.  I am looking for the
name of this style of illustration. This style was used in many
publications of the era; I associate it with a lot of books and
posters oriented towards kids. I sure hope someone out there can help
me.

This is no real answer, but I don't believe that style has an official
name, but it's reminiscent of the playful and cartoony illustration
style common in the 60s. The closest thing I remember to that style is
the cartoon 'Tumbleweeds,' which was wildly popular at the time, and
is probably derivitave of that, at least partially.

http://www.tumbleweeds.com/

I may have been too literal. I meant the style of illustration was
represented by the F-Troop logo (an example of which I cannot find
online), but the content of such illustrations was by no means limited
to western themes or characters. It is simply a large drawing in which
many, many, many things are going on at the same time, usually for
comic purposes. Imagine a drawing, as a Bosch painting, in which there
are numerous cartoonish characters, all of whom are doing different
funny things, none of which are related. The impression I got from the
few examples I remember is that you are not supposed to take one look
at the drawing and see it for what it is; rather the artist intends
for you to stop, to look at the entire drawing and see how many little
scenes he has crammed in there.  I also remember that the scene was
"framed" somehow, in that all the characters were contained within a
structure or a specific scene - in the F-Troop example, all the action
is taking place in around the parade ground of the fort. I also
remember this style of illustration being used in maps, like an
amusement park map.  I am sorry to be so vague about this, but the
style seemed to be in vogue for such a short time that I cannot recall
more examples.

I once worked in an advertising agency where this style of
illustration was referred to as "vignettage." This French word has
other meanings, particularly in reference to photography.