Andrew Hodges hosts a set of web pages devoted to Alan Turing.
The classic paper by Alan Turing `Computing Machinery and Intelligence' is available on-line (though the page it is posted at does not make clear the copyright status.)
Since 1991 the Loebner prize has run in an attempt to stimulate interest in attempts to pass the Turing test. The particularly interesting part of this is the publication of transcripts of entries from 1995 to 1997, although sadly not of the human `contestants'.
There has been a lot of criticism of the Loebner prize in AI circles. The 1996 winner, Jason Hutchens, has written an article called `How to Pass the Turing Test by Cheating' (Technical Report TR97-05, Centre for Intelligent Information Processing Systems, Department of Electrical and Electronic Engineering, The University of Western Australia). With Jason's kind permission I am posting a copy of this paper here in postscript format, in two-up postscript format (cheaper if you want to print it out) and in gzipped postscript format. The transcripts of Jason's 1996 winning entry to the Loebner prize are here.
You can talk on the Web with a view versions of Eliza the Doctor. For example ELIZAneth of Eliza implemented as a Java Applet.
Some of my suggested readings have more on the Turing test and the philosophy of AI.