The short answer to your question is that each of these three methods of reading bits of a file have different use cases. As noted above, f.read() reads the file as an individual string, and so allows relatively easy file-wide manipulations, such as a file-wide regex search or substitution.
f.readline() reads a single line of the file, allowing the user to parse a single line without necessarily reading the entire file. Using f.readline() also allows easier application of logic in reading the file than a complete line by line iteration, such as when a file changes format partway through.
Using the syntax for line in f: allows the user to iterate over the file line by line as noted in the question.
(As noted in the other answer, this documentation is a very good read):
Note: It was previously claimed that f.readline() could be used to skip a line during a for loop iteration. However, this doesn’t work in Python 2.7, and is perhaps a questionable practice, so this claim has been removed.