see Kortlandt (1972) for discussion on the development of the phoneme in Soviet phonological theory, also Freeman (1935) for an idea of the issues at hand in the early days of American Structuralism.
American linguists today tend to be either uncritical about a definition or openly hostile to the concept:
Gussenhoven & Jacobs (1998: 55) "The term phoneme is used to refer to the segment category that the various allophones are variants of."
Odden (2005: 43) "In english, [t] and [th] are predictable variants of a single abstract segment, a phoneme, which we represent as /t/. Predictable variants are termed allophones -- the sounds are in complementary distribution because the context where one variant appears is the complement of the context where the other sound appears."
Ladefoged "Vowels and Consonants" (2001: 193--4) "If we are thinking in acoustic terms, even ? is not so far from t. On a spectrogram both correspond to very similar gaps in the pattern. Linguists have a term for a group of similar sounds of this kind. They call it a phoneme...We talk of the difference between kit and pit being the use of the phoneme /k/ as opposed to the phoneme /p/. There is usually no harm in expressing htings this way. But it is important to remember that it is a kind of shorthand. A phoneme is not a single sound but a group of sounds.
Silverman (2006: 215) "For our purposes though, the phoneme is not an entity on any level—functional,
phonetic, psychological, or even metaphorical. Rather, at best, phoneme is merely a
terminological expedient that might capture the functional non-distinctness of any
collection of phonetic properties that allomorphically alternates. And yet, despite its
expedience, I choose to avoid the term altogether, because terminological expedients
have a demonstrated tendency to become reified by their users."
Ladefoged (ms.) "Perhaps the most startling conspiracy — one that seems to have deceived by far
the majority of linguists — is the appearance of phonemes. Accounts of human
behavior in terms of phonemes are nearly always examples of what has been called
the psychologist's fallacy — the notion that because an act can be described in a
given way that it is necessarily structured in that way. As will be shown later,
phoneme size units play only a minor role in human behavioral acts such as normal
speaking and listening. They are, nevertheless, great imaginary objects for use in
describing linguistic aspects of speech."
Goldsmith (1976: 17--8) "The standard linguistic assumption regarding the nature of phonological representations...implies that the process of language acquisition and of perception includes the development of the ability to take a representation and slice it vertically into columns...Let us call this assumption the "Absolute Slicing Hypothesis" ... The assumption of the Absolute Slicing Hypothesis fails...and this failure is in no sense a trivial one."
I'm going to add the index entry for for "Phoneme" in Fischer-Jorgensen (1975) "Trends in phonological theory", since I didn't have that book with me yesterday:
(1) concept and definition of the phoneme as:
an abstractional fictitious unit 6.12
a bundle of distinctive properties (features) 3.3, 6.4, 8.3, 8.4, 8.18, 11.7, 11.25
a class of (non-contrastive) sounds 6.13, 12.10
a family of sounds 4.3
an element of a morpheme 11.3, 11.9
an ideal abstract sound type 12.17
a member of a phonological opposition 3.3, 4.3
a minimum distinctive unit 11.3, 11.7, 11.10, 11.30
a minimum same of vocal feature 6.4
a minimum unit, differentiating signifiers 11.15, 11.18
a notion with differentiating function 11.4
a point in a pattern 2.12
a physical unit 6.11
a psychologically defined unit 2.4, 3.3, 11.3
a purely logical symbol 6.14, 6.15
the realization of a morphon 10.4, 10.6, 10.12, 10.14
a unit based on comparison 11.30
a useless concept 9.67, 9.68 (but cp. 9.70)