When measuring with a ruler divided into mm lines, should I include the lines by themselves or only in between them?
I illustrated the problem. (I took an example of measuring of 10 mm with two long lines just to make my point, but my question is also about 1 mm, 2 mm, etc).
For this answer, I'll be using this terrible excuse of a ruler, where ┃ is the lines indicating each millimeter and the . is just representing the left-most and right-most face of each of those lines
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
As I understand it, you're asking whether you should measure 1 mm as:
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
<------->
(i.e. from outer face to outer face) or as
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
<--->
(from inner face to inner face).
The answer is that both are wrong: what's important is consistency.
It's worth remembering the obvious assertion that 2 mm has to be twice as long as 1 mm.
If you were to measure from outer face to outer face, 2 mm would be less than twice 1 mm. After all, your measurement of 1 mm spans the distance between the lines plus the full width of two lines ($d + 2w$), while 2 mm spans two distances between lines plus the width of only three lines ($2d + 3w$).
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
<------->
<------------->
Inversely, if you measure from inner face to inner face, 2 mm will be more than twice 1 mm, since 1 mm will only be the distance between two lines ($d$) while 2 will be two distances between lines plus the width of a line ($2d + w$).
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
<--->
<--------->
The only way to get 2 mm to be twice 1 mm is to not think in terms of inner/outer faces but in terms of consistency: define if you're going to use the left face, right face or center of the lines and use that for everything.
This way you ensure that going from the left side of 0 to the left side of 2 is equal to the distance from left-0 to left-1 plus from left-1 to left-2 (or the same from the right face of each line, or from the center of each line):
0 1 2 3 4
.┃. .┃. .┃. .┃. .┃.
<----->
<----->
<----------->
You should include the thickness of one total line. In an ideal world, one would measure the the centre of each line (marked 'also correct' below). In this case, you're including half of each line.
It's not always easy to judge the centre of the line on a rough plastic ruler, so, assuming that the lines are of equal width, it may be easier to measure from the left hand side of each line (marked 'correct' below).
As long as you measure from the same place on both lines (left hand side, centre, or right hand side), then you will be OK.
In theory I agree with others, what's important here is consistency, exact values are meant to be at the center of the lines (so measure center to center or maybe easier from left side to left side).
My emphasis here is on "meant to be":
When you measure existing distance you are not supposed to read anything from that ruler more precise then a mm, let it be inner borders of the lines or outer borders you still will read 10 mm and that additional / missing 0.2-0.4 mm are the error of your device, if you need to be more precise you need a different kind of tool.
When you need to draw lines - according to my experience - it's still easiest to use center of lines as reference.
Neither, you should include the thickness of the line at your "zero" point and exclude the line at the termination of your end point.
If you're measuring weeks, you should choose a period that is exactly 168 hours long. You can measure from a particular time of a day, to the same time on the same day of the week (e.g. noon Sunday to noon the next Sunday). Measuring from the beginning of one day, to the end of that day of next week (e.g. the beginning of this Sunday until the end of next Sunday) gives you eight days. Measuring from the end of a day to the beginning of that day of next week gives you six days.
Similarly, when measuring lengths, you should measure from one point in a tick mark to the same part in the next tick mark. If you measure from the beginning of one tick mark to the end of another tick mark, your distance is slightly longer than what you're recording it as. Also, keep in mind that you shouldn't report any significant digits more than the ticks on the ruler (for instance, if mm are marked, don't give a length as 1.3426 m)
But if you're studying music theory, feel free to measure from one note to another note seven notes away, and call it an "octave".
Further reading: https://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error
Here is an image of a real life ruler.
This is the magnification around 1 cm (on a thresholded image to show better a point). You can start to see that some lines are not always straight or full. That is what you'll get in real life (and it gets worse as you get older and you need prescription glasses :-) ).
If you go further down you see, something like the following. Here is about half a cm worth of hi-res picture.
In the fully magnified picture, every
(Like everybody else has answered before me,) Consistency is the key. I.e. you start measuring from one point and continue up to the same next point.
In a way measuring a single mm is like measuring a period in a sinusoidal signal. i.e. if you start from :
If you need better precision that your ruler subdivision (i.e. if you want to measure the 0.1) and you don't have a caliper 
then a work-around is the following:
I think someone should point out that a ruler is only useful to make straight lines. A scale is used to measure distances.
