Stevens' scale typology isn't necessarily some inherent characteristic of the variables, nor even data itself, but of how we treat the information - of what we're using it to mean.
In some circumstances, exactly the same value may be considered ratio, interval, ordinal or nominal, depending on what we're doing with it - it's a matter of what meaning we give the values, which can change from one analysis to the next. Stevens' typology has some value, but it doesn't do to be overly prescriptive about it.
This issue of the importance of scale as meaning dates back at least to Lord (1953), who offered an example where there were both nominal and interval interpretations of the same set of numbers.
This point was even more clearly made by Velleman and Wilkinson (1993), who offer an example of people receiving consecutive numbered tickets on entry to a reception with a prize being awarded to one of the tickets; depending on the use being made of the numbers on the tickets, they have interpretations on all four scales.
So, for example 'did I win?' is a question treating the number as nominal, while 'did I arrive too early to get the winning ticket?' is a question that treats it as ordinal; on the other hand (and I don't think this one is in the paper) using 5 random ticket numbers in order to estimate the number of people in the room would treat them as ratio (e.g. if there were 4 randomly drawn numbers that got consolation prizes, you'd have 5 random numbers altogether from which to estimate total attendance).
They argue that "good data analysis does not assume data types", "Stevens’s categories do not describe fixed attributes of data", "Stevens’s categories are insufficient to describe data scales" and "Statistics procedures cannot be classified according to Stevens’s criteria" (indeed each statement is also a section title).
Criticisms were also offered in several places by Tukey (e.g. in chapter 5 of Mosteller and Tukey's 1977 book Data analysis and regression); Mosteller and Tukey offered a typology -
names, grades (ordered labels), ranks
(starting from 1, which may represent either the largest or smallest), counted fractions (bounded by zero and one, these include percentages), counts (non-negative integers), amounts (non-negative real numbers), balances (unbounded, positive or negative values).
In my own work, I've seen situations where severe problems with analysis were caused by people failing to appreciate the great difference between variables relating to levels (sometimes called 'stock' variables) and flows - a simple example of these types is the difference in the kinds of analysis appropriate for the amounts of water actually in a storage tank in each of a sequence of periods, and the amount of water flowing into it. These would (in some of those cases) both be sub-categories of the Mosteller and Tukey 'amounts' type (and in those same cases, both ratio variables in Stevens' scheme), indicating that issues of typology may be quite subtle, but can still critically impact appropriate analyses.
P.F.Velleman and L.Wilkinson (1993),
"Nominal, Ordinal, Interval, and Ratio Typologies are Misleading,"
The American Statistician, vol.47 no.1 pp.65-72
(a working version seems to be available at the 2nd authors web page here)
Lord, F. (1953),
"On the statistical treatment of football numbers,"
American Psychologist, 8, pp.750-751
(The year of this paper is given wrongly in the references of the version of the Velleman and Wilkinson paper I linked to, but correctly referred to in the body of the paper)