Speaker Identification
There are two main kinds of evidence that can help with speaker identification.
Earwitness identification (sometimes called 'naive speaker identification')
This is auditory speaker recognition of the everyday kind, as when you recognise someone you know by their voice.
Expert speaker comparison (sometimes called 'technical identification')
This is evidence provided by a phonetician (an expert in phonetics) which involves scientific analysis, both auditory and instrumental, of one or more recordings.
Earwitness identification
People are very used to the everyday experience of recognising someone by their voice, eg. on the telephone or in the next room. This gives a sense that speaker identification is easy. However it is rare that we put the accuracy and reliability of such everyday identification abilities to the test. When this is done, it becomes clear that people make mistakes much more often than they think they do. Importantly, a person's confidence in their identification does not always correlate well with their accuracy. This means the accuracy of auditory identification cannot be taken for granted in a critical situation such as a legal case.
That does not mean that earwitness evidence cannot be used. It does mean that earwitness evidence should be evaluated by an independent expert.
In some cases it may be appropriate to test the witness's identification with a 'voice line-up' - or 'voice parade' - in which the witness is asked to pick the relevant voice from among a number of similar voices on a recording. The construction of materials for such a voice line-up is an extremely delicate matter, and certainly requires phonetic expertise. It is essential that there should be no way of identifying the suspect except by the personal characteristics of the voice. For example if some of the voices are reading or reciting and only one is spontaneous speech, or if background noise gives away the recording location of some speakers as a police station - then clearly the test is not a fair one, and could easily be criticised by opponents in a trial.
Expert speaker comparison
Despite common portrayals in the media and entertainment industry, there are serious limitations on the ability of phoneticians to identify taped voices - or, as is usually the task, to compare an unknown recorded voice with a known recorded voice. It is certainly not a matter of simply making 'voiceprints' which can be compared in the same way as fingerprints.
In fact most phoneticians reject the term 'voiceprint' precisely because it creates this erroneous comparison with fingerprints in people's minds. (The correct term is 'spectrogram'.)
In general, it is considered irresponsible by most professional phoneticians to make highly confident identifications based on this kind of material, unless in very unusual circumstances. (See the IAFPA Code of Practice However there are many cases in which a phonetician can give useful corroborative evidence regarding the identity of a recorded speaker. Each case has to be treated on its merits, as it is rare to find two cases where all the same considerations hold good. For this reason, a phonetician will often prefer to make a preliminary examination of the data and advise on the feasibility of the task before making any commitments as to their ability to reach a conclusion.
It should also be borne in mind that this type of phonetic analysis is very time consuming, requiring painstaking preparation of speech samples and close observation of their acoustic and other characteristics - and often considerable statistical analysis as well. It is usually not feasible to do a full scale analysis at very short notice.
Finally, such analysis should only ever be done by a qualified phonetician who is well-versed in the particular issues involved in voice identification (rather a minority specialisation even among speech experts). There have been cases of underqualified people being used to give this type of evidence. Not only do such cases bring bad repute to the discipline of phonetics, but it is generally easy for the opposition to discredit the evidence.
Here is a short article that gives some general background on speaker identification. It is a little old but I think most of the main issues still hold true. Other useful articles are available through the 'Links' and 'References' sections.
Fraser, H. 1996. Identifying Taped Voices - What phonetic science can and can't do. Policing Issues and Practices Journal 4:39-43.
Here is a more detailed overview by Prof Andy Butcher Forensic Phonetics: Issues in speaker identification evidence
Presentation of Evidence
It is critical that any speaker comparison evidence be presented in appropriate statistical terms. Phil Rose has worked hard to publicise the relevant principles of Bayesian analysis. A current discussion about the applicability of Bayes' theorem in forensic speaker identification can be found in the following links
French, Peter, and Philip Harrison. 2007. Position Statement concerning use of impressionistic likelihood terms in forensic speaker comparison cases. International Journal of Speech Language and the Law 14:137-144.
Rose, Philip, and Geoffrey Stewart Morrison. submitted. A response to the UK Position Statement on forensic speaker comparison. International Journal of Speech Language and the Law.